Question

Mandy and Jeff start running around the track in the same direction at the same time. Mandy runs one lap in 2 minutes and 30 seconds; Jeff runs it at 2 minutes and 15 seconds. If they both start at 8:30 am, at what time will they be side-by-side again?

Answer 1

At 8:52:30 am they will be side-by-side again

Explanation:

Let s be the distance ran in one 1 lap.

Here Jeff runs one extra lap compared to Mandy for coming side by side again.

Mandy runs one lap in 2 minutes and 30 seconds = 150 s

Speed of Mandy,
`=(s)/(150)`

Jeff runs one lap in 2 minutes and 15 seconds = 135 s

Speed of Jeff,
`=(s)/(135)`

Let t be the time when Jeff run one extra lap,

That is

`t* (s)/(135)-t* (s)/(150)=s\\\\t\left ( (1)/(135)-(1)/(150)\right )=1\\\\t* (15)/(135* 150)=1\\\\t=1350s`

So after 1350 seconds Jeff comes side by side to Mandy,

They both start at 8:30 am

1350 s = 22.5 minutes = 22 minutes 30 seconds

Time = 8:52:30 am