SOLUTION: Roger can run one mile in 16 minutes. Jeff can run one mile in 14 minutes. If Jeff gives Roger a 1 minute head start, how long will it take before Jeff catches up to roger? How far

Question 455673: Roger can run one mile in 16 minutes. Jeff can run one mile in 14 minutes. If Jeff gives Roger a 1 minute head start, how long will it take before Jeff catches up to roger? How far will each have run?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Roger can run one mile in 16 minutes. Jeff can run one mile in 14 minutes. If Jeff gives Roger a 1 minute head start, how long will it take before Jeff catches up to roger? How far will each have run?
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Roger DATA:
rate = 1/16 mile/minute ; time = x minutes distance = rt = x/16 miles
------
Jeff DATA:
rate = 1/14 mile/minute ; time = x-1 minutes ; distance = rt = (x-1)/14 miles
=============================================
Equation:
distance = distance
x/16 = (x-1)/14
14x = 16x-16
2x = 16
x = 8 minutes (Roger time)
Roger will run rt = (1/16)8 = 1/2 mile
x-1 = 7 minutes (Jeff time)
Jeff will run rt = (1/14)7 = 1/2 mile
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Cheers,
Stan H.
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