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

Answer:Step-by-step explanation:Let "s" be the the speed of the car taking   the shorter route in [tex]\frac{mi}{hr}[/tex],Let "s-2"  the speed of the cat taking the   longer route in [tex]\frac{mi}{hr}[/tex],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:[tex]d=s{\times}5[/tex]                      (1)and Equation for car taking the longer route is given as:[tex]d+43=(s-2){\times}6[/tex]               (2)Now, substitute equation (1) in (2), we get[tex]5s+43=6s-12[/tex]⇒[tex]43+12=s[/tex]⇒[tex]s=55[/tex]Therefore, equation (1) becomes,[tex]d=5s=5(55)=275[/tex]Thus, the shorter route is =275 miles and the longer route is =d+43=275+43= 318 miles.