Question

On a highway a wreck occurred and caused a 8 mile

traffic jam on one side of the road. The average car is
13.5 feet in length and the average truck is 20 feet in
length. 75% of the traffic jam consists of cars and 25% of
trucks. If the average distance between vehicles is 3 feet,
how many vehicles are stuck in the traffic jam?

Answer 1

1647

Explanation:

Given the following information:

Length of traffic = 8 miles

Average Length of vehicles on the road :

Cars = 14.5 feets

Trucks = 21 feets

18 Wheeler tractor = 73 Feets

% distribution of the different vehicles :

Cars = 70% = 0.7

Trucks = 20% = 0.2

18 wheeler tractor = 10% = 0.1

Distance between vehicles = 4feets

Number of vehicles stuck in the traffic :

Let number of vehicles = v

Summation of (number of vehicles * length of each vehicle) + distance between each vehicle = Length of traffic

Total distance between each vehicle = 4(v-1)

(0.7v * 14.5) + (0.2v * 21) + (0.1v * 73) + 4(v - 1) = 8 miles

1 mile = 5280

8 miles = (5280 * 8) = 42,240

10.15v + 4.2v + 7.3v + 4v - 4 = 42240

25.65v = 42240 + 4

25.65v = 42244

v =42244 / 25.65

v = 1646.939

v = 1647.