Henry I. answered • 11/16/15

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Make a chart for d = rt problems, using actual values and the relative values. For example, the return speed (18 mph slower) gives the expression r-18.

D R T

OUT 72 r t

-------------------------------------

BACK 72 r-18 t+9

Since you want to know r, we need to eliminate t from the equations.

We know through d = rt that t = d/r or 72/r

We can now substitute 72/r for t and solve the equation

I'll let you do some of the simplification, but start with 72 = (r-18)(t+9)

Sub in our rewritten expression for t:

72 = (r-18)[(72/r) + 9]

Simplify and foil till you get

9r

^{2}-162r-1296=0Solve using any of the methods you know for quadratics.

r = 24 and r = -6

The -6 solution is extraneous and can be ignored, since we don't have negative speeds.

ANS = 24mph

Check: D = rt So if r = 24, then 72=24t Give t = 3

Check for the return trip: 18 mph slower = 6 mph 9 hours longer gives 12 hours. Since 6 x 12 = 72, this is the correct solution.