Question

A boat race takes place in Detroit every summer. The first boat to travel 3 miles upstream and back will win the race. If the river has a current of 4mph, what is the speed of the boat in still water, if the winner of the race took a total 1 hour?

Answer 1

Answer:

The speed of the boat in still water u = 8 $\frac{mi}{hr}$

Step-by-step explanation:

Let speed of the boat = u $\frac{mi}{hr}$

Speed of the current = v $\frac{mi}{hr}$ = 4 $\frac{mi}{hr}$

Given that the first boat to travel 3 miles upstream and back in a total 1 hour.

So

$\frac{3}{u - v} + \frac{3}{u + v} = 1$

$\frac{6 u}{u^{2} - v^{2} } = 1$

$u^{2} - v^{2} - 6 u = 0$

Since v = 4

$u^{2} - 6 u - 16 = 0$

By solving above equation

$u^{2} + 2 u - 8 u - 16 = 0$

$u (u + 2) - 8 (u + 2) = 0$

$(u - 8)(u +2) = 0$

u = 8 , - 2

Since u = -2 is not valid.

⇒ u = 8 $\frac{mi}{hr}$

This is the speed of the boat in still water.