SOLUTION: Jon recently drove to visit his parents who live 315 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather)

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Jon recently drove to visit his parents who live 315 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather)      Log On


   

Question 1197658: Jon recently drove to visit his parents who live 315 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 9 hours driving, find the two rates.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
              SPEED      TIME          DISTANCE

GOING TO       r+24      315/(r+24)       315

RETURNING      r         315/r            315

TOTAL                     9

315%2Fr%2B315%2F%28r%2B24%29=9---------simplify and solve.

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35%2Fr%2B35%2F%28r%2B24%29=1

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35%28r%2B24%29%2B35r=r%5E2%2B24r
70r%2B35%2A24=r%5E2%2B24r
r%5E2%2B24r-70r=35%2A24
r%5E2-46r=35%2A24
r%5E2-46r-840=0
r=%2846%2B-+sqrt%2846%5E2%2B4%2A840%29%29%2F2
r=%2846%2B-+sqrt%285476%29%29%2F2
r=%2846%2B74%29%2F2
highlight%28r=60%29

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Could also been done by factoring