SOLUTION: The posted speed on a highway is 65 miles per hour. Car A is 40 feet long. Car B is 20 feet long. If car A is in the lead traveling at 60 mph and car B is 50 feet behind car A

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Question 148845: The posted speed on a highway is 65 miles per hour.
Car A is 40 feet long. Car B is 20 feet long.
If car A is in the lead traveling at 60 mph and car B is 50 feet behind car A traveling at 65 mph, how many feet will it take for car B to pass and gain a 50 foot lead on car A without exceeding the speed limit?
Please show me the formula to solve this.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The posted speed on a highway is 65 miles per hour.
Car A is 40 feet long. Car B is 20 feet long.
If car A is in the lead traveling at 60 mph and car B is 50 feet behind car A traveling at 65 mph, how many feet will it take for car B to pass and gain a 50 foot lead on car A without exceeding the speed limit?
:
Car B will have to travel: 50 + 40 + 50 + 20 = 160 ft to get around Car A
:
Therefore, in the same time frame:
Car B, at 65 mph, will have to travel 160 ft further than Car A travels at 60 mph.
:
Find speeds in ft/sec
%28%2865%2A5280%29%29%2F3600 = 95.33 ft/sec
%28%2860%2A5280%29%29%2F3600 = 88 ft/sec
:
Let d = dist traveled by Car B
then
(d-160) = dist traveled by Car A
:
Write a time equation: Time = dist%2Fspeed
:
Car B time = Car A time
d%2F93.33 = %28%28d-160%29%29%2F88
Cross multiply
:
93.33(d-160) = 88d
:
93.33d - 14932.8 = 88d
:
93.33 - 88d = 14932.8
:
5.33d = 14932.8
d = 14932.8%2F5.33
d = 2,802 ft traveled while car B passes car A