In a 2000 m race, Gates
gives Steve a headstart of 200 m and beats him by 30s. When Gates gives Steve a
headstart of 3 mins he gets beaten by 1000m. How long would Gates and Steve
take to run the race individually?
Answer: Gates – 4 mins and Steve – 5 mins.
Explanation:
Let the speeds of Gates
and Steve be ‘g’ and ‘s’ respectively.
In the first case, since
Gates gives Steve a headstart of 200m Steve has to run only 1800m. It is also
known that Gates finishes the race 30s before Steve. Hence, the time that Steve
takes to run 1800m is the time that Gates takes to run 2000m plus 30s (0.5 min).
1800/s = 2000/g + ½ - - -
- - - - - - - - - - - (1)
In the second case, Gates
gives Steve a headstart of 3 mins and gets beaten by 1000m. Hence while Steve
runs 2000m Gates runs only 1000m. We also see that the time taken by Steve to
run a distance of (2000-3s) is equal to the time taken by Gates to run a
distance of 1000m.
2000/s – 3 = 1000/g - - -
- - - - - - - - - - - - (2)
Solving (1) and (2), we
get
s = 400m/min and g =
500m/min.
So to run a distance of
2000m Steve and Gates would take 5 min and 4 min respectively.