A and b run a 1 km race. if a gives b a start of 50 m, 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.
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So here the only given quantity is 14 sec. 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
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
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