Having a hard time setting up the question for solving.

Question

I'm having a hard time setting up the problem for solving it. 

Shawn's Corvette travels 400 miles averaging a certain speed. If the car had gone 20mph faster, the trip would have taken 2 hours less. Find Shawn's average speed.

Answer 1

Hi Rachel

Corvette-My favorite car !!

 

distance-rate*time

400=r*t

400=(r+20)*(t-2)

400=rt --------> 400/t=r

substitute

400=([400/t]+20)(t-2)

400=([400+20t]/t)(t-2)

multiply both sides by t

400t=(400+20t)(t-2)

400t=400t+20t^2-800-40t

cancel the two 400t's on each side

0=20t^2-40t-800

divide both sides by 20

0=t^2-2t-40

t^2-2t-40=0

using the quadratic formula

(2±√(4+160))/2

(2±√164)/2

(2+12.80625)/2

14.80625/2

t=7.403125 hours

400=r*7.403125

400/7.403125=r

r=54.031237 mph  (round as you like)

if Shawn went 74.031237 mph... (20 mph faster)

400=74.031237*t

400/74.031237=t

t=5.4031246 hours which is 2 hours less than 7.403125 hours

Shawn's average speed was 54.031237 mph