A northbound train and a southbound train meet each other on

A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 6 miles per hour faster than the southbound train. After 1.5 hours, they are 213 miles apart. At what speeds are the two trains traveling?

Solution

The northbound train travels 6 miles per hour faster than the southbound train.

let speed of southbound train is x miles / hour

so speed of northbound train would be (x + 6) miles / hour

distance travelled by south bound train in 1.5 hours = 1.5x

distance travelled by northbound train in 1.5 hours = 1.5 ( x+6) = 1.5x + 9

total distance between them after 1.5 hours = 213 miles

so equation would be

1.5x + 1.5x + 9 = 213

3x + 9 = 213

3x = 204

x = 68

south bound train travels at a speed of 68mph

and north bound train travels at a speed of 68+6 = 74mph