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Question

Nicky and Cristina begin running a race at the same time, though Nicky begins the race 36 meters ahead of Cristina. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

A
15 seconds
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B
18 seconds
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C
25 seconds
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D
30 seconds
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E
45 seconds
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Solution

The correct option is E 30 seconds
Initially, Nicky runs 36 meters at a rate of 3 meters per second. Therefore, Nicky runs for 36/3=12 seconds before Christina starts running.
Save time on this problem by dealing with the rate at which the distance between Cristina and Nicky changes. Nicky is originally 36 meters ahead of Cristina. If Nicky runs at a rate of 3 meters per second and Cristina runs at a rate of 5 meters per second, then the distance between the two runners is shrinking at a rate of 53=2 meters per second.
You can now figure out how long it will take for Cristina to catch Nicky using a single RT=D equation.The rate at which the distance between the two runners is shrinking is 2 meters per second, and the distance is 36 meters (because that's how far apart Nicky and Cristina are):
2t=36
t=18
Nicky's total time is 30 seconds: 12 seconds+18 seconds=30 seconds.

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