Question 971429
Let A's speed be a m/sec and B's be b m/sec, and lap length be l,
Then for A, {{{a*45 = l}}} -(i)
In 25seconds,
Distance covered by A = 25*a and
Distance covered by B = 25*b
Since both meet every 25 seconds,
So, both combinedly cover the distance equivalant of 1 lap,
So, {{{25*a+25*b=l}}}
Putting value of a from eqn (i),
{{{25*(l/45)+25*b=l}}}
=> {{{25*b=l-(5/9)*l}}}
=> {{{25*b = (4/9)*l}}}
=> {{{(l/b) = 25*9/4}}}
=> {{{(l/b) = 225/4}}}
So, time taken by B to run a lap = lap length/B's speed
= l/b
= 225/4 seconds