Question

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 1

D1 = 275 miles

D2 = 318 miles

Explanation:

D=R*T

D1 = be the shorter route

R1 = speed of the car in the shorter route

T1 = time it took to cover shorter route

D2 = the longer route

R2 = speed of the car in the longer route

T2 = time it took to cover longer route

D1 + 43 = D2 (1)

R2 = R1 -2 (2)

R2 = D2/T2 = x2/6

R1 = x1/T1 = x1/5

This means that

R2 = R1 -2 =>

D2/6 = D1/5 -2

The system of equations results

a. D1 -D2 = -43

b. D1/5 - D2/6 = 2

Solving this system of equations, we find that

D1 = 275 miles

D2 = 318 miles

Answer 2

x1 = 275 miles (shorter)

x2 = 318 miles (longer)

Explanation:

Let

x1 = be the shorter route

v1 = speed of the car in the shorter route

t1 = time it took to cover shorter route

x2 = the longer route

v2 = speed of the car in the longer route

t2 = time it took to cover longer route

x1 + 43 = x2 (1)

v2 = v1 -2 (2)

v2 = x2/t2 = x2/6

v1 = x1/t1 = x1/5

This means that

v2 = v1 -2 =>

x2/6 = x1/5 -2

The system of equations results

a. x1 -x2 = -43

b. x1/5 - x2/6 = 2

Solving this system of equations, we find that

x1 = 275 miles

x2 = 318 miles