Quandaries and Queries

Hiya my name is nina. This question was on some practise UKMT test and is for people in school year 7-11 so is a secondary question.

After a years training, Minnie Midriffe increased her average speed in the london marathon by 25%. By what percentage did her time decrease?

I know it has something to do with s=d/t but why would her time decrease?


Hi Nina,

The length of the london marathon is fixed, it doesn't change from year to year. Because of her training Minnie can now run faster so it takes her less time to complete that marathon.

You are correct about the expression "s=d/t", speed is distance over time, but I want to write it as speed times time is distance, that is

s t = d This expression is true before her training (old s) (old t) = d and after her training (new s) (new t) = d d is the same in both expressions, the distance doesn't change.

What you know is that her new speed is 25% more than her old speed. 25% is 1/4 so her new speed is 1 1/4 times her old speed. But 1 1/4 = 5/4, and hence (new s) =  5/4 (old s). Thus

(new s) (new t) = d is  5/4 (old s) (new t) = d

Puting the two red equations together gives

(old s) (old t) = d =  5/4 (old s) (new t) Divide both sides by (old s) to get (old t) = 5/4 (new t) or  4/5 (old t) = (new t)

 4/5 is 80% so her time has decreased by 20%.


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