Each week Lance drives two routes, route A and route B.

One week he drives route A five times and route B twice.

He drives a total of 181 miles that week.

The week after, he drives route A twice and route B three times.

He drives a total of 112 miles that week.

Find the length of each route.

The length of Route A is 29 miles; and

The length of Route B is 18 miles

Step-by-step explanation:

Let the distance taken on route A=x

Let the distance taken on route B=y

One week he drives route A five times and route B twice. He drives a total of 181 miles that week.

Therefore: 5x+2y=181

The week after, he drives route A twice and route B three times. He drives a total of 112 miles that week.

Therefore: 2x+3y=112

We solve the two equations simultaneously for values of x and y.

5x+2y=181

2x+3y=112

Multiply the first equation by 3 and the second equation by 2.

15x+6y=543

4x+6y=224

Subtract

11x=319

x=29

Substitute x=29 in any of the equations to solve for y

5x+2y=181

5 (29) + 2y=181

2y=181-145

2y=36

y=18

Therefore:

The length of Route A is 29 miles; and

The length of Route B is 18 miles