A boat travels 12km upstream and back in 1 hour 45 minutes. If the speed of the current is 3km/h throughout, find the speed of the boat in still water.

Question

Please help me solve this question.

Answer 1

1h+45min=1.75h=(7/4)h    and  use  t=d/v

t_u=12/(v+3),  t_d=12/(v-3)   and the total time    t_u+t_d=7/4   so

12/(v+3) +  12/(v-3) = 7/4   cross multiply  [12(v-3)+12(v+3)] /(v+3)(v-3) =7/4

 

-->  24v/(v+3)(v-3) =7/4   -->   24v=(7/4)(v+3)(v-3)  --> 96v=7(v²-9)

-->  96v=7v²-63   -->   7v²-96v-63=0

solve using the quadratic formula

v=[96±(96²-4*7*(-63))^1/2]/14    the positive root gives    v=14.3km/h