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
Nov 8, 2015

Answer:

#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.