a math question

[formula_2002]

a math question.
Here is a well phrased question presented to me by a PA member.
I not only gave him an answer, but also an excel file to calculate similar problems.
I’m curious how others may try to solve the problem.
So if inclined, please present here .
Thanks.
ps, I dont have any idea what the 2xxx numbers really mean.




using Equibase format in hundreds

1 1/8race
6f time 112.66
finish time 150.32

horse
3 1/2 lengths back at 6fur
1 1/4 back at finish

112.66
.70 (3.5*.2=.70)
113.36 horses time at 6furlongs



150.32
.25(1.25*.2=.25)
150.57horses time at finish

113.20=2893
113.4=2870

150.40=2965
150.60=2941


Now how you come up with the EXACT four digit number between 2893 and 2870, and between 2965 and 2941 ? Will it be a constant multiplier that I could use between any two numbers to get the EXACT number at different timed races?

[Greyfox]

I'm not a math teacher so I won't pretend to be able to solve it, although if my life were on the line I'd find a way.

My guess is that you are not going to come up with a constant multiplier.
The problem appears to be one that requires a curvilinear solution so some squaring will be involved.

[OTM Al]

Everything you've done looks linear, though since I've no idea what these 4 digit numbers are, that is hard to tell, but you can do the simple interpolation. Just looking at the 100ths

(36-20)/(40-20)=.8
2893-2870 = 23
.8*23 = 18.4
2870 + 18.4 = 2888.4

[ryesteve]

My answer would be (d) Not enough information to answer this question

But if I had to, yes, I would use a constant, because even though in the sample given, a fifth is worth 23 points at 6f and 24 points at 9f, I wouldn't assume that the intent is to make a fifth worth different amounts at different distances; my assumption is that in the small piece that was given, this one point difference was due to rounding. I don't believe that if you looked at the full translation table that two seconds would be worth 230 points at 6f and 240 points as 9f.

[ryesteve]

2870 + 18.4 = 2888.4At this point, you needed to substract 18.4 from the higher number, not add it to the lower number...

[OTM Al]

Nope. Otherwise the first calculation would have been

(40-36)/(40-20)

That way works too and perhaps is the way you were taught. Justy depends on what endpoint you work from.

[ryesteve]

That way works tooNo, there's only one answer, and yours isn't it. Just get away from the calculations, and look at the numbers for a second. 113.36 is a lot closer to 113.40 than it is to 113.20, so your answer has to be a lot closer to 2870 than to 2893, not vice versa.

[formula_2002]

113.2 2893
113.36 2874.599884
113.4 2870


150.4 2965
150.57 2944.599917
150.6 2941


the high lighted figures are what i calculated.
they are based on the angle of the slope.

[OTM Al]

No, there's only one answer, and yours isn't it. Just get away from the calculations, and look at the numbers for a second. 113.36 is a lot closer to 113.40 than it is to 113.20, so your answer has to be a lot closer to 2870 than to 2893, not vice versa.

Oops you are right. I thought the bigger number was with the bigger time. Hard to scroll back and forth and write at the same time...

so it would be

2893 - 18.4 = 2874.6

[formula_2002]

Oops you are right. I thought the bigger number was with the bigger time. Hard to scroll back and forth and write at the same time...

so it would be

2893 - 18.4 = 2874.6
that looks like we got the same answer.
you did yours a lot faster..
But I have come to accept my tardiness :)
I need graphs...