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December 30th, 2016, 12:25 PM   #1
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Stuck on a word problem!

Hi everyone,

I am not a Maths whizz at all but would like to help my son with a problem. We are both really stuck... I'd not only like the answer but, more importantly, the method I need to solve it.

Here is the question:

Mark is running steadily round a track. He completes 5 laps in 4 minutes.
Julian is also running steadily round the track, in the same direction. He completes 4 laps in 5 minutes

a) At 10:00am exactly, Julian is just ahead of Mark on the track. By 10:15, how many times will Mark have overtaken Julian?

On another day, Mia is running steadily around the track. She does one lap every 60 seconds. Gareth is running steadily round the track in the opposite direction.

b) If they meet each other every 24 seconds, how long does it take Gareth to do a lap of the track?

Can anyone help?

Thanks!
carriemc is offline  
 
January 2nd, 2017, 07:55 PM   #2
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a) So by 10:15, they will have been running for 15 minutes.
Mark has 18.75 laps since 15/4 sets of 5 laps.
Julian has 12 laps since 3 5 minute sets with each 5 minute being 4 laps.
We have to round down since Mark has not passed Julian, so the number of times overtaken is 18-12 = 6.
b) I will set the speed in seconds. Mia runs 1/60 of the track in 1 second. Gareth runs at x speed. 24 x (1/60 + x) = 1. (The one represents a whole track). His speed is 1/40 track per second. Therefore, it takes Gareth 40 seconds to run a track.

Hopefully, these are right.

Last edited by skipjack; January 2nd, 2017 at 09:43 PM.
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