Maths problem

[nogojoe]

If I have a horse that runs 1200 metres in 1 minute and 15 seconds. (Full pace)

What time will the horse take to run 1100 metres at threequarter pace ?

[Deozaan]

The horse takes 75 seconds to run 1200 meters. That is 0.0625 seconds per meter.
At that pace, it will take 68.75 seconds to run 1100 meters.

Now is the tricky part.

Running the 1100 meters at 0.75 pace would take about 51.5 seconds. (EDIT: The correct answer is about 91.6 seconds.)
But if it's a quarter horse running at three quarter horse pace then it will only take about 23 seconds.

[nogojoe]

Hi Deozaan

thanks for your reply 

The tricky part is running 3/4 pace should make the horse go slower over the distance of 1100m

I see you have done a  68.75 divided by 4 multiplied by 3  to get 51.5 secs.

Should it be 68.75 - 51.5 =17.25 + 68.75 = 86 secs  (1100mts at 3/4 pace)

I'm still trying to get my head around it 

[ConstanceJill]

Hey there.

Unless I'm mistaken, 1200 metres in 75 seconds means a speed of 1200/75 = 16 metres per second
3/4 of that speed is 16*0.75 , that is 12 metres per second
To run 1100 metres at 12 metres per second, it should take 1100 / 12 that is about 91.6 seconds

Another way to think about it is as follows:

Full pace for 1200 is 75 seconds.
If you change the length of the run to 1100 instead of 1200, that's equivalent to multiplying by 11/12.
And if you run at 3/4 the pace, then indeed it should take 4/3 the time.
75 * (11/12) * (4/3) also equals about 91.6

[nogojoe]

Hi ConstanceJill.


I will go with that explanation

[Deozaan]

The tricky part is running 3/4 pace should make the horse go slower over the distance of 1100m

I see you have done a  68.75 divided by 4 multiplied by 3  to get 51.5 secs.

Sorry! I got so caught up in making the quarter horse joke--where I was expecting the number to be lower/faster--that I didn't notice that I accidentally multiplied 68.75 seconds by 0.75 instead of dividing by it. 🤦‍♂️

68.75 / 0.75 gives about 91.6, which is the same answer ConstanceJill came to using other methods, which admittedly are easier to follow.

The correction in full (showing my work this time):

The horse takes 75 seconds to run 1200 meters. That is 0.0625 seconds per meter. (75 / 1200 = 0.0625)
At that pace, it will take 68.75 seconds to run 1100 meters. (0.0625 * 1100 = 68.75)
Running the 1100 meters at 0.75 pace would take about 91.6 seconds. (68.75 / 0.75 = ~91.66667)

[nogojoe]