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On a highway a wreck occurred and caused a 12 mile traffic
jam on one side of the road. The average car is 13.5 feet in
length, the average truck is 20 feet in length, and the
average 18 wheeler tractor trailer is 75 feet in length. 65%
of the traffic jam consists of cars, 20% trucks, and 15% 18
wheeler tractor trailers. The average distance between
vehicles is 2.5 feet. How many cars are in the traffic jam ?
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Let x be the number of cars in the jam (the unknown value under the problem's question).
Then the total length of the jam, from the first bumper to the last bumper, is
0.65*x*13.5 + 0.20*x*20 + 0.15*x*75 + (x-1)*2.5 feet.
It is exactly 12 miles, or 12*5280 = 63360 feet.
So, you have this equation
0.65*x*13.5 + 0.20*x*20 + 0.15*x*75 + (x-1)*2.5 = 63360,
or
24.025x + 2.5x - 2.5 = 63360
26.525x = 63360 + 2.5 = 63362.5
x = 63362.5/26.525 = 2388.784 before rounding and 2489 after rounding.
ANSWER. 2489 vehicles, in total; of them, 0.65*2489 = 1553 (rounded) are cars.
Solved.