An express train and a local train both leave Lake City at 1

An express train and a local train both leave Lake City at 12:00 noon and head for Chicago 60 miles away. The express train travel twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.

Solution

Local train DATA:
rate = x mph ; distance = 60 miles; time = 60/x hrs
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Express train DATA:
rate = 2x mph ; distance = 60 miles ; time = 60/(2x) = 30/x hrs.
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Equation:
local train time - express train time = 2 hrs
60/x - 30/x = 2
Multiply thru by x to get:
60 - 30 = 2x
30 = 2x
x = 15 mph (rate of the local train)
2x = 30 mph (rate of the express train)