Problema Solution

T, S, AND R RUN ON A 400 METER TRACK.

T RUNS 2 minutes per lap

S RUNS 2 minutes 15 seconds per lap

R runs 2 minutes 30 seconds per lap

How far has T gone when S first catches up to R?

Answer provided by our tutors

we will assume that the running track is oval.


v1 = 2 min/lap the speed of T


v2 = 2 min 15 sec/lap = 2 + 15/60 min/lap = 2.25 min/lap the speed of S


v3 = 2 min 30 sec = 2.5 min/lap the speed of R


let


t = the time S needs to catch up on R


d = the number of laps that S will make


d + 1 = the number of laps R will make


since distance = speed*time


v2*t = d


v3*t = d + 1


plug the values for v2, v3 we have:


2.25t = d


2.5t = d + 1


by solving the above system of equations we find:


d = 9 laps


t = 4 min


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S first catches up on T after 4 min.


In 4 min T will make: v1*t = 2*4 = 8 laps.