find the rates

Question

Justin drove to visit his parents 864 miles away. on his way there his speed was 21 miles per hour faster than on his way home. if Justin spent no more than 24 hours driving. find the two rates:

 mph on way to parents house and mph on way home

Answer 1

Let x = Justin's speed on the way home, mph

Justin's speed on the way to his parents was 21 mph faster than the speed on the way home.

Therefore, the speed on his way to his parents is (x + 21)

 

Calculate time to the parents.

  t1 = 864/(x+21)

Calculate time back home.
  t2 = 864/x

 

The total time is 24 hours, therefore  t1 + t2 = 24.

864/(x+21) + 864/x = 24

Divide through by 864.

1/(x+21) + 1/x = 1/36

 

(x + x+21)/[x(x+21)] = 1/36

(2x+21)/(x^2+21x) = 1/36

Cross multiply.

x^2+21x = 36(2x+21)

x^2+21x = 72x+756

x^2 - 51x - 756 = 0

 

Solve with the quadratic formula.

x = (1/2)(51 +/- [(-51)^2 - 4(-756)]^0.5)

x = 0.5(51 +/- 5625^0.5)

x = 63, or x = -12

 

Reject negative answer because it is meaningless.

Therefore x = 63 mph

 

Answer:

Speed on the way to parents = 63+21 = 84 mph  (this should land him in jail).

Speed back home = 63 mph.