To travel 92 miles, it takes Sue 3 hours less time than it takes Doreen to travel 49 miles. Sue travels 16 miles per hour faster than Doreen.

Question

Find the times and rates for both girls Doreen and Sue such that the answer will read...

Doreen......mph for..........hours

Sue...........mph for..........hours

Answer 1

49 = x * t

92 = (x+16)(t-3) = xt + 16t - 3x - 48

140 = xt + 16t - 3x

140 = 49 + 16t - 3x

91 = 16t - 3x

(91 + 3x)/16 = t

49 = (91 +3x)/16 * x

49 * 16 = (91 +3x)x

784 = 91x + 3x^2

3x^2 + 91x - 784 = 0

(3x + 112)(x - 7) = 0

x=7

Dorren: 7 mph for 7 hours = 49 miles

Sue: 23 mph for 4 hours = 92 miles