Two cars are traveling on two different routes, one 43 miles longer than the other. the car traveling on the longer route travels 2 miles per hour slower than the other car and it takes it 6 hours for the trip. if the car with the shorter route takes 5 hours for its trip, find the length of each route. plz asap, due tonight

Step-by-step explanation:

Let "s" be the the speed of the car taking   the shorter route in ,

Let "s-2"  the speed of the cat taking the   longer route in ,

Let "d" be the distance of the shorter route in miles and "d+43" be the distance of the longer route in miles.

Now, Equation for car taking the shorter route is given as:

                     (1)

and Equation for car taking the longer route is given as:

              (2)

Now, substitute equation (1) in (2), we get

⇒

⇒

Therefore, equation (1) becomes,

Thus, the shorter route is =275 miles and the longer route is =d+43=275+43= 318 miles.