Marathon Mission
Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?
Age
14 to 16
Challenge level
Problem
After a year's training, Minnie increased her average speed in the London Marathon by $25\%$.
By what percentage did her time decrease?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 20%
Using inverse operations
100% + 25% = 1 + $\frac14$ = $\frac54$
speed $\times$ time = distance
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(new speed) $\times$ (new time) = distance
$\frac 54 \times$ ? = 1, so ? = $\frac45$ = 80%
80% of original time is a 20% reduction
Using a speed-time graph
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The area on a speed-time graph represents distance.
Yellow rectangle - before 1 year training
Green rectangle - after 1 year training
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Vertical scale factor $\times$ 125% = 1.25
So horizontal scale factor is the inverse
$\div$ 1.25 = $\div \frac54$ = $\times \frac45$ = $\times$ 80%
80% of original time is a 20% reduction
Using algebra
Before: speed $v$ time $\dfrac{26}{v}$
After: speed $\frac54V$ time $\dfrac{26}{\frac54v}$
$=\dfrac{4\times26}{5v}$
$=\dfrac45\times\dfrac{26}v$
80% of original time is a 20% reduction