Maria and Jan are running around an indoor track They leave

Maria and Jan are running around an indoor track. They leave from the same point but jog in different directions at different constant speeds. Maria can run around the entire track in 40 seconds. She meets Jan every 15 seconds. How long does it take Jan to run arount the entire track ?

Solution

distance(d)=rate(r) times time(t) or d=rt;r=d/t and t=d/r
Let t=time it takes Jan to run around the entire track
And let L=length of the track

We are told that Maria can run around the track in 40 sec.
So we know that Maria\'s rate is d/t=L/40
The distance Maria travels in 15 sec =rt=(L/40)*15 or 15L/40 or 3L/8 ft
Together, Jan and Maria can run around the length of the track (L) in 15 sec. So the distance Jan travels in 15 sec=L-distance Maria travels in 15 sec, or
The distance Jan travels in 15 sec =L-3L/8=5L/8 ft
Now we can set up a simple ratio to get to the answer
5L/8 is to 15 sec as L is to t or
(5L/8)/15=L/t simplifying the left side we get
L/24=L/t multiply both sides by 24t
Lt=24L divide both sides by L
t=24 sec--------------------time it takes Jan to run around the track
Ck
Jan\'s rate is L/24
In 15 sec, Jan runs (L/24)*15 or 15L/24 ft
Maria\'s rate is L/40
In 15 sec, Maria runs (L/40)*15=15L/40
15L/24+15L/40=L
3L/8+5L/8=8L/8=L
L=L