Question

The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in 3 hours. What is the speed of the boat in still water?

Answer 1

`3,737` miles/hour.

Explanation:

Let the speed of the boat in still water be `v`.

Therefore total trip is the sum of the upstream part and the downstream part.

Total distance covered is hence `x_t=4m+4m=8m`

But since speed = distance/time, `x=vt`, so we may conclude that
`v_T=x_T/t_T=8/3`mi/hr
and hence write :

`x_T=x_1+x_2`

`therefore v_Tt_T=v_1t_1+v_2t_2`

`therefore 8/3*3=(v-2)t_1+(v+2)t_2`

Also, `t_1+t_2=3`.

Furthermore, `t_1=4/(v-2) and t_2=4/(v+2)`

`therefore4/(v-2)+4/(v+2)=3`

`therefore (4(v+2)+4(v-2))/((v+2)(v-2))=3`

This leads to the quadratic equation in v, `3v^2-8v-12=0`, which upon solving yields `v=3,737 or v=-1,07`.
Clearly the latter is impossible and so hence `v=3,737` is the only feasible solution.