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
• B. $18$ seconds
• C. $25$ seconds
• D. $30$ seconds
• E. $45$ seconds

Answer 1

Answer: (D)

$30$ 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 $5-3=2$ 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: $12seconds+18seconds=30seconds$.