A man swims 12 km upstream and 20 km downstream in 4 hours. He also swims 18…
2024
A man swims 12 km upstream and 20 km downstream in 4 hours. He also swims 18 km upstream and 10 km downstream in 4 hours. What is his speed in still water?
Answer: C. 8 km/h — CONCEPTIf b is the speed in still water and c is the stream speed, then the upstream speed is u = b − c and the downstream speed is d = b + c. Travel time…
- A.
4 km/h
- B.
6 km/h
- C.
8 km/h
- D.
10 km/h
Show answer & explanation
Correct answer: C
CONCEPT
If b is the speed in still water and c is the stream speed, then the upstream speed is u = b − c and the downstream speed is d = b + c.
Travel time equals distance divided by speed. After finding u and d, the still-water speed is their arithmetic mean: b = (u + d)/2.
APPLICATION
Let x = 1/u and y = 1/d. The first journey gives 12x + 20y = 4, and the second gives 18x + 10y = 4.
Subtracting the first equation from the second gives 6x − 10y = 0, so 3x = 5y and x = 5y/3.
Substitute x = 5y/3 into 12x + 20y = 4: 12(5y/3) + 20y = 4, so 20y + 20y = 4 and y = 1/10.
Therefore d = 1/y = 10 km/h. Also, x = 5(1/10)/3 = 1/6, so u = 1/x = 6 km/h.
Hence b = (u + d)/2 = (6 + 10)/2 = 8 km/h.
CROSS-CHECK
With upstream speed 6 km/h and downstream speed 10 km/h, the first time is 12/6 + 20/10 = 2 + 2 = 4 hours, and the second time is 18/6 + 10/10 = 3 + 1 = 4 hours. Both conditions are satisfied, so the speed in still water is 8 km/h.