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.