Leg It

Answer: a) 20 metres, b) 25 metres


Using ratio
a) If Amina runs 100 metres, then the race will be about 12 seconds long. Bhavi needs to run for about 12 seconds.
100 metres in 15 seconds
  20 metres in 3 seconds
  80 metres in 12 seconds
Head start of 20 metres.

b) If Bhavi runs 100 metres, then the race will be about 15 seconds long. Amina needs to run for about 15 seconds.
100 metres in 12 seconds
  25 metres in 3 seconds
125 metres in 12 seconds
Start 25 metres behind Bhavi.


Using distance-time graphs
This distance-time graph shows the race if Amina and Bhavi both start at the same time.  
 
 
a) The graph below shows the race if Bhavi starts in front of Amina
 

The time Bhavi takes is split into 12 and 3. Split the distance axis in the same way.
Share 100 metres in the ratio 12 : 3 = 4 : 1 = 80 : 20
Head start of 20 metres


b) The graph below shows the race if Amina starts behind Bhavi
 

Amina runs for 3 seconds before the start line and 12 seconds after the start line.
3 : 12 = ? : 100
1 : 4 = ? : 100
? = 25, start 25 metres behind