Question

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?

Answer 1

Answer:

Speed of the river = $\frac{4}{3}$ km per hour

Step-by-step 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 = $\frac{\text{Distance}}{\text{Speed}}$

                                           = $\frac{6}{4-v}$ hours

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

Time taken to cover 12 km = $\frac{12}{4+v}$ hours

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

$\frac{6}{4-v}= \frac{12}{4+v}$

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

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v = $\frac{24}{18}$

v = $\frac{4}{3}$ km per hour