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
[tex]0.7n\cdot \:13.5+0.3n\cdot \:20+3n-3=4\cdot \:5280[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:0.7\cdot \:13.5=9.45[/tex]
[tex]9.45n+20\cdot \:0.3n+3n-3=4\cdot \:5280[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:0.3\cdot \:20=6[/tex]
[tex]9.45n+6n+3n-3=4\cdot \:5280[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:9.45n+6n+3n=18.45n[/tex]
[tex]18.45n-3=4\cdot \:5280[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:5280=21120[/tex]
[tex]18.45n-3=21120[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]
[tex]18.45n\cdot \:100-3\cdot \:100=21120\cdot \:100[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]1845n-300=2112000[/tex]
[tex]1845n-300+300=2112000+300[/tex]
[tex]1845n=2112300[/tex]
[tex]\frac{1845n}{1845}=\frac{2112300}{1845}[/tex]
[tex]n=\frac{46940}{41}[/tex]
[tex]n=1144.87804[/tex]
Estimating to get the integer vehicle number and rounding it to the nearest integer.
[tex]n\:\approx \:1145[/tex] vehicles
Therefore, there are approximately 1145 vehicles are stuck in the traffic jam, which is very close to option C.
Keywords: word problem
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