Thread: physics: two cars traveling question

There are Two cars, A and B that are traveling in the same direction, although car A is 193 m behind car B. The speed of A is 27.1 meters per second, and the speed of B is 18.6 meters per seconds. How much time does it take for A to catch B?

in seconds?

anyone who can help me with this please.

For A to catch B, A must travel (193 +x) meters if B travels x meters, both spending the same amount of time.

Distance = speed * time
So, time = distance / speed
t1 = t of A = (193 +x)/27.1
t2 = t of B = x/18.6

t1 = t2
(193 + x)/27.1 = x/18.6
Cross multiply,
(193 +x)(18.6) = 27.1(x)
193(18.6) +18.6x = 27.1x
193(18.6) = 27.1x -18.6x = 8.5x
x = (193*18.6)/8.5 = 422.33 m

Hence,
t = t1 = (193 +422.33)/27.1 = 22.7 sec
t = t2 = 422.33/18.6 = 22.7 sec

Therefore, after 22.7 seconds, A will catch up with B. -----answer.