Kylie went on a 138 mile trip to a soccer game. On the way back, due to road construction she had to drive 23 miles per hour slower. This made the trip take 1 h

Question

Kylie went on a 138 mile trip to a soccer game. On the way back, due to road construction she had to drive 23 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?

Answer 1

d = 138 miles

 

Outbound:

 

vt = 138

 

Inbound:

 

(v-23)(t+1) = 138

 

Get t from vt = 138:

 

t = 138/v

 

Plug this t into (v-23)(t+1) = 138:

 

(v-23)(138/v + 1) = 138

 

Now solve for v:

 

(v-23)(138+v) = 138v

 

138v + v^2 - 3174 - 23v = 138v

 

v^2 - 23v - 3174 = 0

 

v = (1/2) {-(-23) ±√[(-23)^2 - 4(-3174)]}

 

v = (1/2) (23 ± 115)

 

v must be positive, so use only the positive square root:

 

v = (1/2) (23 + 115) = 69 miles per hour