Question

a and b run a 1 km race. if a gives b a start of 50m, a wins by 14 seconds and if a gives b a start of 22 seconds, b wins by 20 meters. find the time taken by a to run 1 km.

Answer 1

So here the only given quantity is 14 sec.So express equations in terms of time.
Let a and b be the speed of A and B respectively.
Given,
When A gives B a head start of 50m,
950/b-1000/a=14-----(1)
The second condition:
980/a+22=1000/b----(2)
Let 1/a=x 1/b=y
then,
950y-1000x=14
980x+22=1000y--->1000y-22=980x
solving we get..
a=10m/s
time taken by A to run 1000km=1000/10=100s

Answer 2

Answer:

Time taken by a to run 1000m is 100s

Step-by-step explanation:

Let the speed of a be x and the speed of b be y.

Now, b with a start of 50m the time taken by a is 1000/x

         the time taken by b is 950/y

let x = 1/a and y = 1/b then we have 950b-1000a = -14.

          b  with a start of 22s we get 980a - 1000b = 22

By solving these two equations we get x = 10m/s .

So a will take 100s to run 1000m