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Question

A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 18 miles per hour faster than the southbound train. After 2 hours, they are 244 miles apart. At what speeds are the two trains traveling?

The north bound train is traveling ___ mph

The south bound train is traveling ___mph

Answer 1

Let r_n = rate or speed of the the train northbound

r_s = rate or speed of the the train southbound

d_n = distance travelled of the the train northbound

d_s = distance travelled of the the train southbound

Since the northbound train travels 18 miles per hour faster than the southbound train, we can represent it this way:

r_n = 18 + r_s 

To solve this problem, we can use the common formula d = rt (distance = rate multiplied by the time travelled). Therefore the distance travelled by the train northbound after t = 2 hours is:

d_n = 2 r_n  or  d_n = 2 (18 + r_s)

Furthermore, the distance travelled by the train southbound after t = 2 hours is:

d_s = 2 r_s  

If we add these two distances together they should add up to 244 miles according to the problem.

2 (18 + r_s) + 2 r_s = 244

36 + 2 r_s + 2 r_s = 244

36 + 4 r_s = 244

r_s = 52 mph

r_n = 18 + r_s = 18 + 52 = 70 mph