SOLUTION: Chloe went on a 168 mile trip to a soccer game. On the way back, due to road construction she had to drive 14 miles per hour slower. This made the trip take 1 hour longer. How fast

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Chloe went on a 168 mile trip to a soccer game. On the way back, due to road construction she had to drive 14 miles per hour slower. This made the trip take 1 hour longer. How fast      Log On


   

Question 1030704: Chloe went on a 168 mile trip to a soccer game. On the way back, due to road construction she had to drive 14 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed in mi/hr going to the game
Let +t+ = her time in hrs going to the game
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equation going to the game
(1) +168+=+s%2At+
Equation for coming back from game
(2) +168+=+%28+s+-+14+%29%2A%28+t+%2B+1+%29+
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(2) +168+=+s%2At+-+14t+%2B+s+-+14+
(2) +168+=+t%2A%28+s+-+14+%29+%2B+s+-+14+
and
(1) +t+=+168%2Fs+
Substitute (1) into (2)
(2) +168+=+%28+168%2Fs+%29%2A%28+s+-+14+%29+%2B+s+-+14+
(2) +168+=+168+-+2352%2Fs+%2B+s+-+14+
(2) +s+-+14+=+2352%2Fs+
(2) +s%5E2+-+14s+=+2352+
Complete the square
(2) +s%5E2+-+14s+%2B+%2814%2F2%29%5E2+=+2352+%2B+%2814%2F2%29%5E2+
(2) +s%5E2+-+14s+%2B+49+=+2352+%2B+49+
(2) +%28+s+-+7+%29%5E2+=+2401+
(2) +%28+s+-+7+%29%5E2+=+49%5E2+
Take the square root of both sides
(2) +s+-+7+=+49+
(2) +s+=+56+
She drove 56 mi/hr to the soccer game
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check:
(1) +168+=+s%2At+
(1) +168+=+56%2At+
(1) +t+=+3+
and
(2) +168+=+%28+s+-+14+%29%2A%28+t+%2B+1+%29+
(2) +168+=+%28+56+-+14+%29%2A%28+3+%2B+1+%29+
(2) +168+=+42%2A4+
(2) +168+=+168+
OK