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
[tex]16\ min=16/60\ h[/tex]
[tex]\frac{10}{x+30} +\frac{2}{x-30}=\frac{16}{60}[/tex]
Multiply by (x+30)(x-30) both sides
[tex]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[/tex]
Multiply by 60 both sides
[tex]16x^2-720x=0[/tex]
Divide by 16 both sides
[tex]x^2-45x=0\\x(x-45)=0[/tex]
The solution is x=45\ mph
