Question

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

upstream at top speed in a total of 16 min. What was the top speed of William's boat if the rate
of the current was 30 mph? (Let x represent the rate of the boat in still water.)

Answer 1

The top speed of William's boat was 45 mph

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`

`(10)/(x+30) +(2)/(x-30)=(16)/(60)`

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

`10(x-30)+2(x+30)=(16)/(60)(x^2-900)\\10x-300+2x+60=(16)/(60)x^2-240\\12x-240=(16)/(60)x^2-240\\(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