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Washing 4 cars and 6 trucks takes 130 minutes. Washing 2 cars and 6 trucks takes 110 minutes. How long does it take to wash each type of vehicle?

A. 33 minutes for a car and 34 minutes for a truck
B. 43.75 minutes for a car and 20 minutes for a truck
C. 34 minutes for a car and 33 minutes for a truck
D. 20 minutes for a car and 43.75 minutes for a truck

1 Answer

4 votes

Final answer:

By setting up a system of linear equations based on the time it takes to wash a number of cars and trucks, we can calculate that it takes 10 minutes to wash one car and 15 minutes to wash one truck.

Step-by-step explanation:

To determine how long it takes to wash each type of vehicle, we set up a system of linear equations. Let c represent the time it takes to wash one car and t represent the time it takes to wash one truck. Using the information given:

  • 4c + 6t = 130 minutes (for washing 4 cars and 6 trucks)
  • 2c + 6t = 110 minutes (for washing 2 cars and 6 trucks)

Now, we will solve this system by subtracting the second equation from the first equation:

  • 4c + 6t - (2c + 6t) = 130 - 110
  • 2c = 20
  • c = 10

So, it takes 10 minutes to wash one car. Next, we substitute the value of c into one of the equations to find t:

  • 2(10) + 6t = 110
  • 20 + 6t = 110
  • 6t = 90
  • t = 15

Therefore, it takes 15 minutes to wash one truck. So, the correct answer is that it takes 10 minutes for a car and 15 minutes for a truck to be washed.


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