SOLUTION: Sierra went on a 200 mile trip to a soccer game. On the way back, due to road construction she had to drive 10 miles per hour slower. This made the trip take 1 hour longer. How fas

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Sierra went on a 200 mile trip to a soccer game. On the way back, due to road construction she had to drive 10 miles per hour slower. This made the trip take 1 hour longer. How fas      Log On


   

Question 1193693: Sierra went on a 200 mile trip to a soccer game. On the way back, due to road construction she had to drive 10 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Basic idea is RT=D for R rate or speed, time T, and distance D.
You may sometimes handle the basic idea like
RT=D
%28RT%29%2FR=D%2FR
T=D%2FR

Your given example allows you to form two expressions of time, and question asks for their difference. 

                SPEEDS        TIMES              DISTANCE

GOING TO        r              200/r                200
RETURN          r-10           200/(r-10)           200

DIFF.                            1

With that you can setup 200%2F%28r-10%29-200%2Fr=1 , and then simplify and solve.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

The number of 200 has two divisors, 40 and 50, that differ by 10 units and such that if you divide 200 by 40 one time


and divide 200 by 50 next time, you will get two quotients, 5 and 4, that differ exactly one units.


By making this mental thought experiment, you quickly will get the answer to your question, without using any equations and much faster.


ANSWER.  The faster rate is 50 miles per hour.

Solved.

Good as a mental exercise . . .