SOLUTION: A moving van gets caught in slow traffic. The driver averages only 30 miles an hour from New York to Chircago. Will he be able to drive fast enough on the way back to make an aver

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Question 418102: A moving van gets caught in slow traffic. The driver averages only 30 miles an hour from New York to Chircago. Will he be able to drive fast enough on the way back to make an average speed of 60 miles an hour for the whole trip? Explain your answer. (Distance between Chicago and New York = 900 miles)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = time for CHI to NY trip
(total distance) / (total time) = (average speed)
given:
Time for NY to CHI trip is 900+%2F+30+=+30 hrs
+%282%2A900%29+%2F+%2830+%2B+t%29+=+60
+1800+=+60%2A%2830+%2B+t%29+
1800+=+1800+%2B+60t
60t+=+0
t+=+0
In order to average 60 mi/hr for the 1800 mi trip,
the driver must make it back in 0 hours. That
means he can't do it. So maybe 60 mi/hr is the upper
limit. What if he wants to average 59 mi/hr?
Can he do it?
+1800+%2F+%2830+%2B+t%29+=+59
+1800+=+59%2A%2830+%2B+t%29
1800+=+1770++%2B+59t
59t+=+30
t+=+30%2F59
t+=+.508
Yes, but he'll have to make it back in about 1/2 hr
His average speed on the return trip would be:
900%2F.508+=+1771.65 mi/hr
Well, no cops could catch him if he survived the
acceleration and deceleration.
He would have to average quite a bit lower
speed on the return trip.