Nina went on a 72 mile trip to a soccer game. On the way back, she had to drive 18 miles ..... How fast did she drive to the soccer game?

Question

Nina went on a 72 mile trip to a soccer game. On the way back, due to road construction she had to drive 18 miles per hour slower. This made the trip take 9 hours longer. How fast did she drive to the soccer game?

Answer 1

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

 

9r²-162r-1296=0

 

Solve 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.