SOLUTION: On Jerry's way to work in the morning, he was only able to travel at a rate of 20 mph because of traffic. On his drive home, he averaged 40mph. If his total time was 1 1/2 hours, h
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Question 482696: On Jerry's way to work in the morning, he was only able to travel at a rate of 20 mph because of traffic. On his drive home, he averaged 40mph. If his total time was 1 1/2 hours, how long did it take him to drive to work?
Found 2 solutions by Alan3354, cleomenius:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
On Jerry's way to work in the morning, he was only able to travel at a rate of 20 mph because of traffic. On his drive home, he averaged 40mph. If his total time was 1 1/2 hours, how long did it take him to drive to work?
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His average speed for the round trip is
Avg = 2*20*40/(20 + 40) = 1600/60 = 80/3 mph
The distance = (80/3) * (3/2) * (1/2) = 20 miles
His time going was 20/20 = 1 hour
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Return time = 20/40 = 1/2 hour
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Not the usual way of working it.
Here's the proof of the round-trip calculations.
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r1 = rate going
r2 = rate returning
t = d/r1 + d/r2 (total time for round trip of distance 2d)
t = (d*r1 + d*r2)/(r1*r2) = 2d*(r1 + r2)/r1*r2
Avg = 2d/t
--> Avg = 2*r1*r2/(r1 + r2) (similar to parallel resistors or parallel flows, but x2)
The average speed is less than the average of the 2 speeds (unless they're equal), because more time is spent at the lower speed.
Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
I would set this up in the following manner with two equations:
rate*time = rate*rime
20x = 40y
x + y = 1.5;
y = 1.5 - x
Then substitute equation two into equation one.
20x = 40(1.5- x)
20x = 60 - 40x
60x = 60
x = 1
y therefore comes out to .5
Cleomenius.
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