Alex is motorboat took four hours to make a trip down stream with a 5 mph current. The return trip against the same current took six hours. Find the speed of the boat in Stillwater and the distance he traveled.

25 mph

120 miles

Step-by-step explanation:

We have that the speed is equal to:

v = d / t

if we solve for distance:

d = v * t

in this case, since it is the same route both outward and back, the distances are equal, therefore:

v1 * t1 = v2 * t2

t1 = 4 hours

t2 = 6 hours

v1 = x + 5 (downstream speed)

v2 = x -5 (upstream speed)

replacing:

(x + 5) * 4 = (x - 5) * 6

4 * x + 20 = 6 * x - 30

6 * x - 4 * x = 20 + 30

2 * x = 50

x = 25

speed is 25 mph

now the distance would be:

d = (25 + 5) * 4 = 120

d = (25 - 5) * 6 = 120

In other words, the route was 120 miles.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

answer:   expression= p+p*d%

price reduction + sale price = $625

sale price: $p+$p*d%

where d% is the percentage of discount

step-by-step explanation:

original price = p

price went down by $150 price reduction $p*d%

sale price= $ 475

therefore the price before sale is: $625

and the expression that shows the price before sale is: p+p*d%