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# distance rate problem?

To travel 100 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 42 miles riding a bicycle. Sue travels 18 miles per hour faster than Doreen. Find the times and rates of both girls.

### 1 Answer

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- ranjankarLv 79 years agoFavorite Answer
LET DOREEN'S SPEED BE X MPH

SUE'S SPEED = (X+18 ) MPH

42 / X - 100/ ( X+18) = 2

42 ( X+18) -100X = 2 ( X^2 + 18X)

21 ( X +18) - 50X = X^2 + 18X

21X + 378 -50X = X^2 + 18X

X^2 + 47X - 378 = 0

X^2 - 7X + 54X -378 = 0

X ( X-7) +54 ( X -7) = 0

( X-7) ( X+54) = 0

X = 7MPH

ANSWER DOREEN = 7MPH TIME TAKEN = 6 HOURS

SUE = 25MPH TIME TAKEN = 4 HOURS

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