A boat goes 8 km upstream and then returns

Asked by admin @ 23/08/2021 in Math viewed by 322 People

A boat goes 8 km upstream and then returns. Total time taken is 4 hours 16 minutes. Velocity of the current is 1 km / hour. Actual velocity of the boat is

Answered by admin @ 23/08/2021

Let the velocity of the boat be x

time taken for upstream motion = $\frac{8}{x-1}$
time taken for downstream motion = $\frac{8}{x+1}$

Total time =
$\frac{8}{x-1}+\frac{8}{x+1} = \frac{16x}{x^{2}-1} = 4 \frac{16}{60} = \frac{64}{15} \\ \\
cross\: multiplying \\ \\
240x = 64x^{2}-64 \implies 64x^{2}-240x-64 = 0 \\ \\
x = 4 km/h$

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