Math Is Fun Forum

TARAJS

Member

Registered: 2011-12-01

Posts: 19

Kids walking around a track at different speeds

Three children start walking together from a starting line around a 250-meter long circular track. the first child walked at a speed of 5 km/hr, the second child at 4 km/hr, and the third child at 3 km/hr. how many minutes elapsed before they were all crossing the starting line at the same time?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Kids walking around a track at different speeds

Hi TARAJS;

These are complicated alignment problems.
They are solved by congruences.
I get after 15 minutes of running they will meet again at the starting point.

You are solving 3 conguences here

this can reduced to

The solution I am getting is t = 900 seconds or 15 minutes.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Kids walking around a track at different speeds

hi TARAJS

Welcome to the forum.

Three children start walking together from a starting line around a 250-meter long circular track. the first child walked at a speed of 5 km/hr, the second child at 4 km/hr, and the third child at 3 km/hr. how many minutes elapsed before they were all crossing the starting line at the same time?

250 meters = 0.25 Km

So child 1 will do a lap in 0.25 / 5 hours = 0.05 hours = 0.05 x 60 minutes = 3 mins.

Doing a similar calculation for the other two gives

child 2 does a lap in 3.75 mins

child 3 does a lap in 5 mins.

So if you wrote out the 'times tables' for 3 and 3.75 and 5 what is the first number that is in all three lists?

15 is obviously the first number in both the 3 and 5 times tables and 4 x 3.75 = 15 as well

so after 15 mins all three will be completing a lap.

At that time child 1 has done 5 laps; child 2 has done 4 laps; child 3 has done 3 laps.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

TARAJS

Member

Registered: 2011-12-01

Posts: 19

Re: Kids walking around a track at different speeds

Thank you all!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Kids walking around a track at different speeds

Hi TARAJS;

You are welcome.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.