When 2 or more people compete to reach a certain point, they are said to be participating in a race.
Start : If one person gives a start to another person, it means that the second person has to run less than the first person. For example, if A gives a start of 40 m to B in 100 m race, it means that A will run for 100 m but B will run for 100 – 40 = 60 m.
Question 1 : In a 100 m race, A beats B by 28 metres. Also, at the finish line, A was 7 seconds ahead of B. Find the time taken by A to complete the race. Solution : According to the question, B covers 28 m in 7 seconds.
=> B’s speed = 28 / 7 = 4 m/s
=> Time required by B to complete 100 m = 100 / 4 = 25 s
Now, A needs 7 s less than B to complete the race.
=> Time required by A = 25 – 7 = 18 s
Question 2 : In a 100 m race, A can give a start of 4 m to B and 6.4 m to C. How much start can B give to C ? Solution : If A covers 100 m, B covers 96 m and C covers 93.6 m
=> When B covers 96 m, C covers 93.6 m
=> When B covers 100 m, C covers (93.6 / 96) x 100 = 97.5 m
Therefore, B can give a start of 100 – 97.5 = 2.5 m to C.