Posted by **john** on Sunday, September 16, 2012 at 4:11pm.

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

- college algebra -
**Henry**, Monday, September 17, 2012 at 5:24pm
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.

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