You may also like

problem icon

Mediant Madness

Kyle and his teacher disagree about his test score - who is right?

problem icon

Tyneside Average Speed

Can you work out the average speed of the van?

problem icon

Average Surroundings

Can you work out Ali's age based on the diagram?

Marathon Mission

Age 14 to 16 Short Challenge Level:

Answer: 20%


Using inverse operations
100% + 25% = 1 + $\frac14$ = $\frac54$

    speed      $\times$      time      = distance
      $\times \frac54$              $\times$ ?            $\times$ 1 because distance does not change
(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

The area on a speed-time graph represents distance.


Yellow rectangle - before 1 year training

Green rectangle - after 1 year training
 
The rectangles have the same area since the distance is still the same

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

 
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.