Question

On a windy day William found that he could travel 10 mi downstream and then 2 mi back

Answer 1

Answer:

The top speed of William's boat was 45 mph

Step-by-step explanation:

Let

x -----> represent the rate of the boat in still water in mph

we know that

The speed or rate is equal to divide the distance by the time

speed=distance /time

time=distance/speed

Downstream

speed=(30+x) mph

distance=10 mi

time1=10/(30+x)

Upstream

speed=(x-30) mph

distance=2 mi

time2=2/(x-30)

The sum of the time downstream plus the time upstream must be equal to 16 minutes

Convert minutes to hours

$16\ min=16/60\ h$

$\frac{10}{x+30} +\frac{2}{x-30}=\frac{16}{60}$

Multiply by (x+30)(x-30) both sides

$10(x-30)+2(x+30)=\frac{16}{60}(x^2-900)\\10x-300+2x+60=\frac{16}{60}x^2-240\\12x-240=\frac{16}{60}x^2-240\\\frac{16}{60}x^2-12x=0$

Multiply by 60 both sides

$16x^2-720x=0$

Divide by 16 both sides

$x^2-45x=0\\x(x-45)=0$

The solution is x=45\ mph