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37 votes
A paddleboat can move at a speed of 4 ​km/h in still water. The boat is paddled 12 km downstream in a river in the same time it takes to go 6 km upstream. What is the speed of the​ river?

A paddleboat can move at a speed of 4 ​km/h in still water. The boat is paddled 12 km-example-1
User HeXor
by
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1 Answer

28 votes
28 votes

Answer:

Speed of the river =
(4)/(3) km per hour

Explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km =
\frac{\text{Distance}}{\text{Speed}}

=
(6)/(4-v) hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km =
(12)/(4+v) hours

Since, time taken by the boat in both the cases is same,


(6)/(4-v)= (12)/(4+v)

6(4 + v) = 12(4 - v)

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v =
(24)/(18)

v =
(4)/(3) km per hour

User Levar
by
2.8k points