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
click here to see the step by step solution of the system of equations:
S first catches up on T after 4 min.
In 4 min T will make: v1*t = 2*4 = 8 laps.