SOLUTION: Jessie recently drove to visit her parents who live 756 miles away. On her way there her average speed was 21 miles per hour faster than on her way home (she ran into some bad weat

Let x be the slower rate, in miles per hour (mph).
Then the faster rate is (x+21) mph.

Jessie spent  hours for the way "there".
She spent  hours for the returning trip.

The condition says

 = 21.

Solve for x. For it, multiply both sides by x*(x+21). You will get

756x + 756*(x+21) = 21x*(x+1).

Divide both sides by 21. You will get

36x + 36(x+21) = x*(x+1).

Simplify and solve this quadratic equation.

Let speed to the house be S

Then return-trip speed = S - 21

We then get the following TIME equation: 

756(S - 21) + 756S = 21S(S - 21) --- Multiplying by LCD, S(S - 21)

 ---------- Dividing both sides by 21









S(S - 84) - 9(S - 84) = 0

(S - 84)(S - 9) = 0

S, or speed to the house =            OR           S = 9 (ignore)

Speed on return trip: 84 - 21, or