Question

5. A train travels two different routes: the North Route and the South Route. • On Monday, the train traveled the North Route 8 times and the South Route 10 times, traveling a total of 410 miles. • On Tuesday, the train traveled the North Route 15 times and the South Route 11 times, traveling a total of 575 miles. How long is each route?

Answer 1

North Route is 20 miles, and South Route is 25 miles.

Explanation:

Let the length of the North route be represented by x and that of the South route be represented by y.

On Monday,

8x + 10y = 410

On Tuesday,

15x + 11y = 575

So that,

8x + 10y = 410 .............. 1

15x + 11y = 575 ......... 2

Using substitution method, from equation 1;

x =
`(410 - 10y)/(8)` ................. 3

Substitute the expression for x into equation 2,

15(
`(410 - 10y)/(8)`) + 11y = 575

multiply through by 8,

6150 - 150y + 88y = 4600

6150 - 62y = 4600

6150 - 4600 = 62y

1550 = 62y

divide through by 62 to have,

y = 25

Substitute the value of y in equation 3

x =
`(410 - 10y)/(8)`

=
`(410 - 10(25))/(8)`

= 20

x = 20

Thus, North Route is 20 miles, and South Route is 25 miles.