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

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