SOLUTION: Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole t

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Question 553934: Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole trip?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Joe drove at the speed of 45 miles per hour for a certain distance.
He then drove at the speed of 55 miles per hour for the same distance.
What is the average speed for the whole trip?
:
Let d = distance driven at each speed
then
2d = distance of the whole trip
:
let a = the average speed for the whole trip
:
Write a time equation; time = dist/speed
:
45mph time + 55mph time = total time
d%2F45 + d%2F55 = %282d%29%2Fa
Multiply by the LCM of 45 and 55, 495a
495a*d%2F45 + 495a*d%2F55 = 495a%282d%29%2Fa
cancel the denominators;
11ad + 9ad = 495(2d)
20ad = 990d
divide both sides by d
20a = 990
a = 990/20
a = 49.5 mph is the average speed for the trip
:
;
:
Let's check this out, using an assigned distance of 200 mi
100%2F45 + 100%2F55 = %28200%29%2F49.5
2.22 + 1.82 = 4.04
4.04 = 4.04; confirms our average speed of 49.5 mph