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by Cindy Donaldson
Topics: Math, Test Prep, High School
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  1. Fill in the blanks with variables that you can find in the problem. In our problem, the speed of the Express is defined in terms of the Freight.

 

 
Distance (in miles)
Rate (in mph)
Time (in hours)
Freight Train
d
r
2
Express Train
d + 40
2r -30
2

 

  1. Use the distance formula to make two equations based on the table:

d = r * t

Freight Train:
d= r * 2
d = 2r

Express Train: (d + 40) = (2r-30) * 2

d + 40 = 4r – 60

  1. Substitute and Solve:

Since the first equation tells us that d = 2r, we can substitute that in the second equation for the Freight Train:

d + 40 = 4r – 60 becomes 2r + 40 = 4r – 60
                                                2r = 100
                                                r = 50

The Freight Train is going 50 mph.

Therefore, the Express is going 2(50) –30 = 70 mph.