Question

The current of a river is 3 miles per hour. A boat travels to a point 16 miles upstream and back in 4 hours. What is the speed of the boat in still water ? The speed of the boat in still water is ?

Answer 1

let the speed of boat in still water be v miles/hr

Speed of boat while travelling upstream = v-3
Speed of boat while travelling downstream = v+3

time taken while travelling upstream = 16 / (v-3)
time taken while travelling downstream = 16 / (v+3)

total time = 16 / (v-3) + 16 / (v+3)
4 = (16(v+3) + 16 (v-3))/(v^2-9)
4(v^2 - 9) = 16v + 48 + 16v - 48
4v^2-36 = 32v
4v^2 - 32v - 36 = 0
v^2 - 8v - 9 = 0
v^2 - 9v + v - 9 = 0
v(v-9)+1(v-9) = 0
(v+1)(v-9) = 0
v = -1 or v=9
since v can’t be negative
v = 9 miles/hr

Answer: 9 miles/hr