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.)

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

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

Multiply by 60 both sides

Divide by 16 both sides

The solution is x=45\ mph

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0