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

Answer 1

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 = (Y-4) hrs(d = 132mi).
Eq2: (X+15)(Y-4) = 132.

In Eq2, substitute 56/X for Y:
(X+15)(56/X-4) = 132
56-4x+840/x-60 = 132
-4x+840/x-4 = 132
Multiply both sides by X:
-4x^2+840-4x = 132x
-4x^2-136x+840 = 0
Divide both sides by -4:
x^2+34x-210 = 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.
Y-4 = 10.5-4 = 6.5 hrs = Sue's hrs.