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?
:
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
{{{((65*5280))/3600}}} = 95.33 ft/sec
{{{((60*5280))/3600}}} = 88 ft/sec
:
Let d = dist traveled by Car B
then
(d-160) =  dist traveled by Car A
:
Write a time equation: Time = {{{dist/speed}}}
:
Car B time = Car A time
{{{d/93.33}}} = {{{((d-160))/88}}}
Cross multiply
:
93.33(d-160) = 88d
:
93.33d - 14932.8 = 88d
:
93.33 - 88d = 14932.8
:
5.33d = 14932.8
d = {{{14932.8/5.33}}}
d = 2,802 ft traveled while car B passes car A