Question 909925
rate * time = distance


13 minutes divided by 60 = .2166... hours.


rate * time = distance for the truck is 60 * x = d, where d is the distance the car travels and x is the time it takes to travel that far in hours.


rate * time = distance for the car is 66 * (x-.2166...) = d, where d is the distance the car travels and (x-.2166...) is the time it takes to travel that far in hours.


when the car has caught up with the truck, they have both traveled the same distance.


since rate * time = distance, this allows you to set rate * time for the truck equal to rate * time for the car.


you get:


60 * x = 66 * (x-.2166...)


solve for x in equation to get x = 2.3833... hours.


the truck has traveled for 2.3833... hours and the car has traveled for 2.3833... - .2166... hours which is equal to 2.166... hours.


since rate * time = distance, then:


the distance the truck has traveled is 60 * 2.3833.... = 143 miles.


the distance the car has traveled is 66 * 2.166... = 143 miles.


It will take the car 2.166... hours to pass the truck and the car will do it in 143 miles.


2.166... hours is equivalent to 2.166... * 60 minutes which is equal to 130 minutes.