Question

A boat traveled 390 miles downstream and back. the trip downstream took 13 hours. the trip back took 39 hours. what is the speed of the boat in still water? what is the speed of the current?

Answer 1

Speed of boat in still water is `20\ \text{miles/hr}` &

Speed of water current is `10\ \text{miles/hr}`

Explanation:

Let `V_B` miles/hr be the speed of boat in still water & `V_C` be the speed of current.

Now, the time taken by boat to travel a distance `390` miles downstream with a relative velocity `V_B+V_C` is given as

`\frac{390}{V_B+V_C}=13`

`V_B+V_C=30\ ......(1)`

Similarly, the time taken by boat to travel a distance `390` miles upstream with a relative velocity `V_B-V_C` is given as

`\frac{390}{V_B-V_C}=39`

`V_B-V_C=10\ ......(2)`

Adding (1) & (2) we get

`V_B+V_C+V_B-V_C=30+10`

`2V_B=40`

`V_B=20`

setting the value of `V_B` in (1), we get

`20+V_C=30`

`V_C=10`

Hence, the speed of boat in still water is `20\ \text{miles/hr}` &
the speed of water current is `10\ \text{miles/hr}`