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?

1 Answer
Trevor Ryan.
Nov 8, 2015

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.

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