Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40mph and Train B at 50mph. Train A passes a station at 9:20 am. If train B passes the same station at 9:32 am, at what time will train B catch up to train A?
let the time passed from 9:32 til train B catches up to A be t hrs.
When B passes the station, train A will have traveled 12 minutes at 40 mph or 40(12/60) miles or 8 miles.
So when B catches A,
train A is (8 + 40t)miles past the station
train B is 50t miles past the station
but these two distances are the same, so
50t = 8 + 40t
10t = 8
t = 8/10 hours = 48 minutes
so the meet at 9:32 + 0:48
= 10:20 am
To find the time at which train B catches up to train A, we can use the concept of relative speed.
The relative speed between train A and train B is the difference between their speeds. In this case, the relative speed is 50 mph (train B's speed) minus 40 mph (train A's speed), which is 10 mph.
Given that train B passes the station at 9:32 am, which is 12 minutes (or 0.2 hours) after train A passed the station, we need to determine how long it takes for train B to catch up to train A at a relative speed of 10 mph.
To find the time it takes, we can use the formula:
Time = Distance / Speed
Since the trains are traveling in the same direction, the distance between them is the initial distance between them when train B passes the station, which can be calculated as the product of train A's speed and the time difference between their respective passing times:
Distance = 40 mph * 0.2 hours = 8 miles
Now, using the formula Time = Distance / Speed, we can find the time it takes for train B to catch up to train A:
Time = 8 miles / 10 mph = 0.8 hours
Therefore, train B will catch up to train A 0.8 hours (or 48 minutes) after train B passes the station at 9:32 am.
To find the catching up time in relation to the initial time when train A passed the station (9:20 am), we need to add 0.8 hours to 9:32 am:
9:32 am + 0.8 hours = 10:12 am
So, train B will catch up to train A at 10:12 am.