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Dynamics- collision of cars problem

The problem is like this
Assume both cars A and B are intially travelling to the right at 98 ft/s. Car A is tailgating leaving very little room between car A and car B. At that instant driver of car B notices a n accident and starts to break witha deceleration of 2o ft/s^2. By the time the driver of car A notices the distance betwwen them has reduced to 22.5 ft and the velocity of car B is slowed down to 78 ft/s. Assume that the driver of car A immediately puts the brakes and it takes him only 0.5 s to apply breaks. The car decelerates with 30 ft/s^2. Calculate when collision occurs and relative speed of collision.

I have already solved the problem. attaching the solution. can anyone let me know if i am correct or wrong
 

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rude man

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The problem is like this
Assume that the driver of car A immediately puts the brakes and it takes him only 0.5 s to apply brakes. /QUOTE]

Which is it? Does he immediately apply the brakes or does it take him 0.5s to apply the brakes?
 
He applies the break after 0.5 s
 

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