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.
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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
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