Question

On a residential single lane road there was a wreck that backed up traffic for 4 miles. 70% of the traffic consists of cars and 30% of the traffic consists of trucks. the average distance between vehicles is 3 feet. the average length of a car is 13.5 feet and the average length of a truck is 20 feet. estimate how many vehicles are stuck in the traffic jam.
(hint: there are 5280 feet in 1 mile)


A) 276
B) 896
C) 1172
D) 1412

Answer 1

Answer:

There are approximately 1145 vehicles are stuck in the traffic jam. It is very close to option C.

Step-by-step explanation:

To determine:

Estimate how many vehicles are stuck in the traffic jam.

Information Fetching and Solution Steps:

• On a residential single lane road there was a wreck that backed up traffic for 4 miles.

• 70% of the traffic consists of cars and 30% of the traffic consists of trucks.

• The average distance between vehicles is 3 feet.

• The average length of a car is 13.5 feet.

• The average length of a truck is 20 feet.
• There are 5280 feet in 1 mile

Let 'n' be the total number of vehicles stuck in the traffic jam.

So, the equation becomes

$0.7n\cdot \:13.5+0.3n\cdot \:20+3n-3=4\cdot \:5280$

$\mathrm{Multiply\:the\:numbers:}\:0.7\cdot \:13.5=9.45$

$9.45n+20\cdot \:0.3n+3n-3=4\cdot \:5280$

$\mathrm{Multiply\:the\:numbers:}\:0.3\cdot \:20=6$

$9.45n+6n+3n-3=4\cdot \:5280$

$\mathrm{Add\:similar\:elements:}\:9.45n+6n+3n=18.45n$

$18.45n-3=4\cdot \:5280$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:5280=21120$

$18.45n-3=21120$

$\mathrm{Multiply\:both\:sides\:by\:}100$

$18.45n\cdot \:100-3\cdot \:100=21120\cdot \:100$

$\mathrm{Refine}$

$1845n-300=2112000$

$1845n-300+300=2112000+300$

$1845n=2112300$

$\frac{1845n}{1845}=\frac{2112300}{1845}$

$n=\frac{46940}{41}$

$n=1144.87804$

Estimating to get the integer vehicle number and rounding it to the nearest integer.

$n\:\approx \:1145$ vehicles

Therefore, there are approximately 1145 vehicles are stuck in the traffic jam, which is very close to option C.

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