SOLUTION: Julie recently drove to visit her parents who live 200 miles away. On her way there her average speed was 9 miles per hour faster than on her way home (she ran into some bad weathe

Question 1148884: Julie recently drove to visit her parents who live 200 miles away. On her way there her average speed was 9 miles per hour faster than on her way home (she ran into some bad weather). If Julie spent a total of 10 hours driving, find the two rates.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52879)   (Show Source): You can put this solution on YOUR website!
.

Let the slower average speed be x miles per hour. Then the faster average speed is (x+9) miles per hour. The time equation is + = 10 hours. Solve it. Your first step is to multiply both sides by x*(x+9) to rid of the denominators. You will get a quadratic equation. Reduce it to the standard form and solve by any way you can.

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From this lesson, learn on how to write, how to use and how to solve a "time" equation.

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Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

Certainly you should understand the method for setting up the problem for solving by formal algebra, as shown in the response from the other tutor.

However, if a quick solution by any means is allowed (or desirable, as in a timed competitive exam), then some logical trial and error can get you to the answer much faster than the formal algebra.

(1) The total distance is 400 miles; the total time is 10 hours. So the average rate is 40mph.

(2) The two rates are not the same, so one of them is greater than 40mph and the other is less. And the difference between the two rates is 9mph.

(3) The total driving time is (exactly) 10 hours. That means the two rates a and b must be "nice" numbers, satisfying 200/a + 200/b = 10.

The two "nicest" numbers that are either side of 40 and have a difference of 9 are 36 and 45; so try them....

Done....!
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