0/1 p Samantha went on a 54 mile trip to a soccer game. On the way back, due to road construction she
had to drive 27 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive
to the soccer game?

58 miles per hour.

Step-by-step explanation:

   58 miles per hour on the trip to the soccer game,

   which gives 1 hour for the way "to there" and 2 hours for the way back.

Let r be the speed "to there", in miles per hour.

Then the speed back is (r-29), mph.

The "time" equation is

   58/r-29 - 58/r = 1   hour

Multiply by r*(r-29) both sides.

   58r - 58*(r-29) = r*(r-29)

   58*29 = r^2 - 29r

   r^2 - 29r - 58*29 = 0

   (r+29)*(r-58) = 0.

The roots are -29 and 58, and only positive 58 makes sense.

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