Thread: Stuck on a word problem!

1. Stuck on a word problem!

Hi everyone,

Apologies, I am not at all a Maths whizz but am trying to help my son (age 11) with a Maths problem. I don't just need the answer, I would also like to understand the method to find it so I can explain 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 in5 minutes.

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

On another day, Mia is running steadily around the track. She does one lap every 60seconds. 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 thetrack?

Can anyone help??

Thank you!

2. Re: Stuck on a word problem!

Hey carriemc.

Hint - Try thinking about how to get the distance. Note that distance = speed * time and you have the speed variable.

When it comes to overtaking it means that the remainder when you divide the total distance run by the distance of the track is equal to the distance they are at from the start of the track.

In other words - the remainder of total_distance_run/distance_of_track is equal for both runners.

3. Re: Stuck on a word problem!

Originally Posted by carriemc
Hi everyone,

Apologies, I am not at all a Maths whizz but am trying to help my son (age 11) with a Maths problem. I don't just need the answer, I would also like to understand the method to find it so I can explain it.

Here is the question:

Mark is running steadily round a track. He completes 5 laps in 4 minutes.
So Mark is running at a speed of 5/4 lap per minute.

Julian is also running steadily round the track, in the same direction. He completes 4 laps in5 minutes.
And Julian is running at 4/5 lap per minute.

a) At 10:00am exactly, Julian is just ahead of Mark on the track.
"Just ahead"? How far ahead? I am going to assume that they are really at the same location but we will need to count Mark "overtaking" Julian once right at the start.

By 10:15, how many timeswill Mark have overtaken Julian?
At a speed of 5/4 lap per minute in 15 minutes, Mark will have gone (5/4)(15)= 75/4= 18 and 3/4 laps. In the same time Julian, at 4/5 lap per minute, will have gone (4/5)(15)= 12 laps. 18- 12= 6 and adding that first overtaking that is 7 times.

On another day, Mia is running steadily around the track. She does one lap every 60seconds. 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 thetrack?

Can anyone help??

Thank you!
Mia is running at 1/60 lap per second. If we let v be the rate, in laps per second, at which Gareth is running. Gareth's speed, relative to Mia, is (1/60+ v) laps per second so Gareth takes 1/(1/60+ v)= 60/(1+ 60v) seconds to run a lap, relative to Mia. Since it take 24 seconds to run from "Mia to Mia", 60/(1+ 60v)= 24. Solve that for v.