college algebra
posted by john on .
to travel 132 miles it take sue riding a moped 2 hours less time then it takes doreen to travel 56 miles riding a bike. sue travels 15 miles per hour faster then doreen find the time and rates

Doreen's speed = X mi/h
Doreen's time = Y hrs(d = 56mi).
Eq1: X*Y = 56.
Y = 56/X
Sue's speed = (X+15) mi/h.
Sue's time = (Y4) hrs(d = 132mi).
Eq2: (X+15)(Y4) = 132.
In Eq2, substitute 56/X for Y:
(X+15)(56/X4) = 132
564x+840/x60 = 132
4x+840/x4 = 132
Multiply both sides by X:
4x^2+8404x = 132x
4x^2136x+840 = 0
Divide both sides by 4:
x^2+34x210 = 0.
Use Quad. formula.
X = 5.34 mi/h = Doreen's speed.
X+15 = 5.34+15 = 20.34 mi/h=Sue's speed.
Y = 56/X = 56/5.34 = 10.5 h. = Doreen's
time.
Y4 = 10.54 = 6.5 hrs = Sue's hrs.