SOLUTION: Ryan drove 380 miles in6 hours. He drove at an average rate of 70 miles per hour for the first part of the trip. He averaged 60 miles an hour for the second part. For how many hou

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Question 1115995: Ryan drove 380 miles in6 hours. He drove at an average rate of 70 miles per hour for the first part of the trip. He averaged 60 miles an hour for the second part. For how many hours did he average 70 miles per hour?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
               SPEED          TIME        DISTANCE

PART1          70              x          70x

PART2          60             6-x        60(6-x)

TOTAL                         6            380


highlight_green%2870x%2B60%286-x%29=380%29
Solve this for x, and that is the answer for the question.
-
7x%2B6%286-x%29=38
7x%2B36-6x=38
x=38-36
highlight%28x=2%29----------hours spent at 70 m.p.h.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


There are all kinds of alternatives to the standard algebraic solution method shown by the other tutor. Of course, that method is fine; but here are a couple of alternatives that you might try, if getting to the answer faster is what you want.

(1) logical reasoning...

If he traveled all 6 hours at 60 mph, he would only have gone 360 miles -- not 380. To get those extra 20 miles going 10 mph faster, he has to drive at the higher speed for 20/10 = 2 hours. So he drove at 60 mph for 4 hours and 70 mph for 2 hours.

(2) finding the ratio of times spent at the two speeds by comparing the average speed for the whole trip to the two different speeds...

His average speed was 63 1/3 mph, which is one-third of the way from 60 to 70. That means he spent one-third of his time at the higher speed. So he spent 2 hours at 70 mph, which means he spent 4 hours at 60 mph.