Upstream and downstream speed problems.
45 solved questions · 15 easy · 20 medium · 10 hard
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A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. What is its downstream speed?
Answer: A. 12 km/h
Solution
Downstream speed = u + v = 10 + 2 = 12 km/h Answer: 12 km/h
A boat's speed in still water is 15 km/h and the stream speed is 3 km/h. What is its upstream speed?
Answer: B. 12 km/h
Solution
Upstream speed = u - v = 15 - 3 = 12 km/h Answer: 12 km/h
A man rows downstream at 14 km/h and upstream at 8 km/h. What is his speed in still water?
Answer: C. 11 km/h
Solution
Speed in still water = (downstream + upstream)/2 = (14 + 8)/2 = 11 km/h Answer: 11 km/h
A man rows downstream at 14 km/h and upstream at 8 km/h. What is the speed of the stream?
Answer: D. 3 km/h
Solution
Speed of stream = (downstream - upstream)/2 = (14 - 8)/2 = 3 km/h Answer: 3 km/h
A boat goes 8 km/h in still water and the stream is 2 km/h. How long will it take to go 30 km downstream?
Answer: A. 3 hours
Solution
Downstream speed = 8 + 2 = 10 km/h Time = 30 / 10 = 3 hours Answer: 3 hours
A boat's speed in still water is 12 km/h and the stream speed is 3 km/h. How long will it take to go 36 km upstream?
Answer: B. 4 hours
Solution
Upstream speed = 12 - 3 = 9 km/h Time = 36 / 9 = 4 hours Answer: 4 hours
A man rows 20 km downstream in 2 hours and the same distance upstream in 4 hours. What is the speed of the stream?
Answer: C. 2.5 km/h
Solution
Downstream speed = 20/2 = 10 km/h; upstream speed = 20/4 = 5 km/h Stream speed = (10 - 5)/2 = 2.5 km/h Answer: 2.5 km/h
A boat's speed in still water is 9 km/h and the stream flows at 1 km/h. How far does it travel downstream in 3 hours?
Answer: D. 30 km
Solution
Downstream speed = 9 + 1 = 10 km/h Distance = 10 x 3 = 30 km Answer: 30 km
A boat's speed in still water is 5 km/h and the stream is 1 km/h. How much more time does it take to go 12 km upstream than 12 km downstream?
Answer: A. 1 hour
Solution
Upstream time = 12 / (5 - 1) = 3 h Downstream time = 12 / (5 + 1) = 2 h Difference = 1 hour Answer: 1 hour
A swimmer can swim at 6 km/h in still water. If the stream flows at 1.5 km/h, what is his speed swimming with the stream?
Answer: B. 7.5 km/h
Solution
Speed with the stream = 6 + 1.5 = 7.5 km/h Answer: 7.5 km/h
A boat's downstream speed is 36 km/h. Express this in m/s.
Answer: C. 10 m/s
Solution
36 km/h = 36 x 5/18 m/s = 10 m/s Answer: 10 m/s
A boat can go 10 km/h in still water and the stream speed is 5 km/h. How long does it take to go 15 km upstream?
Answer: D. 3 hours
Solution
Upstream speed = 10 - 5 = 5 km/h Time = 15 / 5 = 3 hours Answer: 3 hours
A man rows at 12 km/h in still water in a river flowing at 4 km/h. How long does he take to row 64 km downstream?
Answer: A. 4 hours
Solution
Downstream speed = 12 + 4 = 16 km/h Time = 64 / 16 = 4 hours Answer: 4 hours
A boat's speed in still water is 20 km/h and the stream is 4 km/h. How far can it go upstream in 2.5 hours?
Answer: B. 40 km
Solution
Upstream speed = 20 - 4 = 16 km/h Distance = 16 x 2.5 = 40 km Answer: 40 km
A boat's speed in still water is 6 km/h more than the stream's speed. If the stream's speed is 2 km/h, what is the boat's upstream speed?
Answer: C. 6 km/h
Solution
Speed in still water = 2 + 6 = 8 km/h Upstream speed = 8 - 2 = 6 km/h Answer: 6 km/h
A man rows at 15 km/h in still water and the stream flows at 3 km/h. He rows to a place and comes back in 5 hours in total. How far is the place?
Answer: D. 36 km
Solution
Downstream speed = 18 km/h, upstream speed = 12 km/h Let distance = d. d/18 + d/12 = 5 (2d + 3d)/36 = 5, so d = 36 km Answer: 36 km
A boat goes 30 km downstream in 3 hours and 18 km upstream in 3 hours. What is the speed of the boat in still water?
Answer: A. 8 km/h
Solution
Downstream speed = 30/3 = 10 km/h; upstream speed = 18/3 = 6 km/h Still water speed = (10 + 6)/2 = 8 km/h Answer: 8 km/h
A boat takes twice as long to go upstream as downstream over the same distance. If the stream speed is 4 km/h, what is the speed of the boat in still water?
Answer: B. 12 km/h
Solution
Time is twice, so upstream speed is half of downstream speed. u - 4 = (u + 4)/2, so 2u - 8 = u + 4, u = 12 km/h Answer: 12 km/h
Shortcut: If upstream time is n times downstream time, u : v = (n+1) : (n-1) = 3 : 1.
A boat covers 16 km downstream in 2 hours and 16 km upstream in 4 hours. What is the speed of the stream?
Answer: C. 2 km/h
Solution
Downstream speed = 16/2 = 8 km/h; upstream speed = 16/4 = 4 km/h Stream speed = (8 - 4)/2 = 2 km/h Answer: 2 km/h
A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. What is the average speed of the boat for a round trip between two points?
Answer: D. 9.6 km/h
Solution
Downstream 12 km/h, upstream 8 km/h. Take distance = 24 km each way. Time = 24/12 + 24/8 = 2 + 3 = 5 h Average speed = 48 / 5 = 9.6 km/h Answer: 9.6 km/h
Shortcut: Average speed for a round trip = (u^2 - v^2)/u = 96/10 = 9.6.
A swimmer's speed in still water is 5 km/h and the stream is 3 km/h. How many times as long does he take to swim a distance upstream as downstream?
Answer: A. 4 times
Solution
Upstream speed = 5 - 3 = 2 km/h; downstream speed = 5 + 3 = 8 km/h Time is inversely proportional to speed, so ratio = 8/2 = 4 Answer: 4 times
A boat's speed in still water is 8 km/h and the stream is 2 km/h. It takes 2 hours more to travel a certain distance upstream than downstream. Find the distance.
Answer: B. 30 km
Solution
Upstream speed = 6 km/h, downstream speed = 10 km/h d/6 - d/10 = 2 d (5 - 3)/30 = 2, so d = 30 km Answer: 30 km
A boat goes 20 km upstream in 4 hours and 12 km downstream in 1.5 hours. What is the speed of the stream?
Answer: C. 1.5 km/h
Solution
Upstream speed = 20/4 = 5 km/h; downstream speed = 12/1.5 = 8 km/h Stream speed = (8 - 5)/2 = 1.5 km/h Answer: 1.5 km/h
A boat with speed 10 km/h in still water goes downstream for 2 hours and then turns back and goes upstream for 1 hour. The stream speed is 5 km/h. How far from the starting point is the boat?
Answer: D. 25 km
Solution
Downstream speed = 15 km/h, upstream speed = 5 km/h Distance downstream = 15 x 2 = 30 km Distance back upstream = 5 x 1 = 5 km Distance from start = 30 - 5 = 25 km Answer: 25 km
A man rows to a place 48 km away and back in 14 hours. He can row 4 km with the stream in the same time as 3 km against it. Find the speed of the stream.
Answer: A. 1 km/h
Solution
Speeds with and against the stream are in the ratio 4 : 3. Let them be 4k and 3k. 48/(4k) + 48/(3k) = 14 12/k + 16/k = 14, so k = 2 Downstream = 8 km/h, upstream = 6 km/h Stream speed = (8 - 6)/2 = 1 km/h Answer: 1 km/h
A boat covers 2 km downstream in 10 minutes and the same distance upstream in 15 minutes. What is its speed in still water?
Answer: B. 10 km/h
Solution
Downstream speed = 2 km in 10 min = 12 km/h; upstream speed = 2 km in 15 min = 8 km/h Still water speed = (12 + 8)/2 = 10 km/h Answer: 10 km/h
A boat takes 4.5 hours to go upstream between two ports and 3 hours to return downstream. If the stream flows at 2 km/h, what is the distance between the ports?
Answer: C. 36 km
Solution
Let still water speed = u and distance = d. d = 4.5 (u - 2) = 3 (u + 2) 4.5u - 9 = 3u + 6, so u = 10 km/h d = 3 x 12 = 36 km Answer: 36 km
In a stream flowing at 3 km/h, a boat takes 5 hours to go 30 km upstream. How long will it take to go 30 km downstream?
Answer: D. 2.5 hours
Solution
Upstream speed = 30/5 = 6 km/h, so still water speed = 6 + 3 = 9 km/h Downstream speed = 9 + 3 = 12 km/h Time = 30/12 = 2.5 hours Answer: 2.5 hours
A boat takes 4 hours to travel 36 km upstream in a stream flowing at 3 km/h. What is the speed of the boat in still water?
Answer: A. 12 km/h
Solution
Upstream speed = 36/4 = 9 km/h Still water speed = upstream + stream = 9 + 3 = 12 km/h Answer: 12 km/h
The speed of a boat in still water is 5 times the speed of the stream. If the boat covers 36 km downstream in 3 hours, what is the speed of the stream?
Answer: B. 2 km/h
Solution
Let stream speed = v, so boat speed = 5v. Downstream speed = 5v + v = 6v = 36/3 = 12 km/h v = 2 km/h Answer: 2 km/h
A man can row 4.8 km/h with the stream and 3.4 km/h against the stream. What is the speed of the stream?
Answer: C. 0.7 km/h
Solution
Speed of stream = (with stream - against stream)/2 = (4.8 - 3.4)/2 = 0.7 km/h Answer: 0.7 km/h
A boat's speed in still water is 8 km/h and the stream flows at 2 km/h. How long will the boat take to go 24 km upstream and return?
Answer: D. 6.4 hours
Solution
Upstream time = 24 / (8 - 2) = 4 h Downstream time = 24 / (8 + 2) = 2.4 h Total = 4 + 2.4 = 6.4 hours Answer: 6.4 hours
A swimmer covers 400 m downstream in 4 minutes and returns the same 400 m upstream in 8 minutes. What is the speed of the stream in km/h?
Answer: A. 1.5 km/h
Solution
Downstream speed = 400/4 = 100 m/min; upstream speed = 400/8 = 50 m/min Stream speed = (100 - 50)/2 = 25 m/min In km/h = 25 x 60 / 1000 = 1.5 km/h Answer: 1.5 km/h
A boat goes 36 km downstream in 3 hours. If the stream flows at 2 km/h, how long will it take to go 40 km upstream?
Answer: B. 5 hours
Solution
Downstream speed = 36/3 = 12 km/h, so still water speed = 12 - 2 = 10 km/h Upstream speed = 10 - 2 = 8 km/h Time = 40/8 = 5 hours Answer: 5 hours
A boat takes 3 times as long to go a certain distance upstream as to come back downstream. If its speed in still water is 10 km/h, what is the speed of the stream?
Answer: C. 5 km/h
Solution
Time upstream = 3 x time downstream, so downstream speed = 3 x upstream speed. 10 + v = 3 (10 - v) 10 + v = 30 - 3v, so 4v = 20 and v = 5 km/h Answer: 5 km/h
Shortcut: If upstream time is n times downstream time, v = u (n - 1)/(n + 1) = 10 x 2/4 = 5.
A boat goes 30 km upstream and 44 km downstream in 10 hours. It goes 40 km upstream and 55 km downstream in 13 hours. What is the speed of the stream?
Answer: D. 3 km/h
Solution
Let upstream speed = x and downstream speed = y. 30/x + 44/y = 10 ... (1) 40/x + 55/y = 13 ... (2) Multiply (1) by 4 and (2) by 3: 120/x + 176/y = 40 and 120/x + 165/y = 39 Subtract: 11/y = 1, so y = 11 km/h; then 30/x = 10 - 4 = 6, so x = 5 km/h Stream speed = (11 - 5)/2 = 3 km/h Answer: 3 km/h
A boat goes 24 km upstream and 36 km downstream in 6 hours, and 36 km upstream and 24 km downstream in 6.5 hours. What is the downstream speed of the boat?
Answer: A. 12 km/h
Solution
Let 1/x = a (upstream) and 1/y = b (downstream). 24a + 36b = 6 and 36a + 24b = 6.5 Add: 60(a + b) = 12.5, so a + b = 5/24 Subtract: 12(a - b) = 0.5, so a - b = 1/24 a = 1/8, b = 1/12 Upstream speed = 8 km/h, downstream speed = 12 km/h Answer: 12 km/h
Two ports P and Q are 60 km apart on a river that flows from P to Q at 2 km/h. At the same moment, one boat leaves P for Q and another leaves Q for P. Both have still-water speed 10 km/h. How far from P do they meet?
Answer: B. 36 km
Solution
Boat from P goes downstream: 10 + 2 = 12 km/h Boat from Q goes upstream: 10 - 2 = 8 km/h They approach at 12 + 8 = 20 km/h, so they meet after 60/20 = 3 h Distance from P = 12 x 3 = 36 km Answer: 36 km
A boat with still-water speed 8 km/h passes a floating log while going upstream in a river that flows at 2 km/h. It continues upstream for 1 hour, then turns round and goes downstream. How far downstream of the point where it first met the log will the boat meet the log again?
Answer: C. 4 km
Solution
Work in the frame of the water: the log is stationary and the boat moves at 8 km/h relative to it. The boat moves away for 1 hour (8 km) and takes 1 hour to return, so they meet 2 hours after the first meeting. In 2 hours the log drifts 2 x 2 = 4 km with the stream Answer: 4 km
Shortcut: The boat takes as long to come back as it spent going away; the log drifts for the total time.
A boat takes 5 hours to go 24 km upstream and 24 km downstream in total. If the stream flows at 2 km/h, what is the speed of the boat in still water?
Answer: D. 10 km/h
Solution
Let still water speed = u. 24/(u - 2) + 24/(u + 2) = 5 24 x 2u / (u^2 - 4) = 5, so 48u = 5u^2 - 20 5u^2 - 48u - 20 = 0, so (u - 10)(5u + 2) = 0 u = 10 km/h (the other root is negative) Answer: 10 km/h
Shortcut: Test the options: u = 10 gives 24/8 + 24/12 = 3 + 2 = 5 hours.
Stream speed is 2 km/h. Boat B (still-water speed 8 km/h) leaves a jetty going downstream. One hour later boat A (still-water speed 10 km/h) leaves the same jetty in the same direction. How far from the jetty does A overtake B?
Answer: A. 60 km
Solution
Downstream speed of B = 8 + 2 = 10 km/h; of A = 10 + 2 = 12 km/h Head start of B = 10 x 1 = 10 km Relative speed = 12 - 10 = 2 km/h, so A catches up in 10/2 = 5 h Distance from jetty = 12 x 5 = 60 km Answer: 60 km
A boat takes 6 hours to go from A to B upstream and 4 hours to return downstream. How long will a log take to float from A to B?
Answer: B. 24 hours
Solution
Let the distance be d (take d = 48 km). Upstream speed = d/6, downstream speed = d/4 Stream speed = (d/4 - d/6)/2 = d/24 Time for the log = d / (d/24) = 24 hours Answer: 24 hours
Shortcut: Time for a log = 2 x (t1 x t2) / (t1 - t2) = 2 x 24 / 2 = 24 hours.
A man rows to a place 6 km upstream and back in 4 hours. He takes the same time to row 2 km against the stream as 6 km with the stream. What is his speed in still water?
Answer: C. 4 km/h
Solution
Same time for 2 km upstream and 6 km downstream, so downstream speed = 3 x upstream speed. Let upstream = p, downstream = 3p. 6/p + 6/(3p) = 4, so 8/p = 4 and p = 2 km/h; downstream = 6 km/h Still water speed = (6 + 2)/2 = 4 km/h Answer: 4 km/h
A boat takes 6 hours to go downstream between two ports and 9 hours to come back upstream. How long would it take to cover the same distance in still water?
Answer: D. 7.2 hours
Solution
Let distance = d. Downstream speed = d/6, upstream speed = d/9 Still water speed = (d/6 + d/9)/2 = 5d/36 Time = d / (5d/36) = 36/5 = 7.2 hours Answer: 7.2 hours
Shortcut: Time in still water = 2 t1 t2/(t1 + t2) = 2 x 6 x 9/15 = 7.2 h.
In still water a boat goes 12 km/h. It covers 40 km upstream in the same time as it covers 60 km downstream. What is the speed of the stream?
Answer: A. 2.4 km/h
Solution
Same time, so upstream : downstream speeds = 40 : 60 = 2 : 3 (12 - v) : (12 + v) = 2 : 3 3 (12 - v) = 2 (12 + v) 36 - 3v = 24 + 2v, so 5v = 12 and v = 2.4 km/h Answer: 2.4 km/h
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