Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and train B is traveling at 60 miles per hour. Train A passes a station at 8:25 p.m. If train B passes the same station at 8:37 p.m. at what time will train B catch up to train A?
Let the time between 8:25 and the moment they meet be t hours
So train B covers the distance from the station to where they meet in 12 minutes less than train A
and 12 minutes = 12/60 or .2 hours
then 60t = 40(t + .2)
solve for t, you should get t=.4hours
which is the same as .4(60) minutes or 24 minutes.
so they will meet at 8:49 pm
I just looked at my definition of t again and according to my equation should have defined it as
Let the time between 8:37 and the moment they meet be t hours
I should then have added the 24 minutes to 8:37 to get a time of
9:01 pm
To find the time when train B catches up to train A, we need to determine the time difference between when train A passes the station and when train B passes the same station.
Given that train A passes the station at 8:25 p.m. and train B passes the same station at 8:37 p.m., the time difference is:
8:37 p.m. - 8:25 p.m. = 12 minutes.
Now, let's convert this time difference from minutes to hours:
12 minutes ÷ 60 minutes/hour = 0.2 hours.
So, the time difference between when train A passes the station and when train B passes the same station is 0.2 hours.
Next, we need to determine the catch-up time for train B. To do this, we'll calculate the distance that train A travels during the catch-up time.
Since train A is traveling at a rate of 40 miles per hour, the distance it covers in 0.2 hours is:
40 miles/hour × 0.2 hours = 8 miles.
Therefore, train B needs to cover an additional 8 miles to catch up to train A.
Now, we can determine the catch-up time for train B. Since it is traveling at a faster speed than train A, we'll subtract their speeds:
60 miles per hour - 40 miles per hour = 20 miles per hour.
To calculate the catch-up time, we divide the additional distance (8 miles) by the relative speed (20 miles per hour):
8 miles ÷ 20 miles per hour = 0.4 hours.
Finally, we add this catch-up time to the time when train B passes the station:
8:37 p.m. + 0.4 hours = 9:07 p.m.
Therefore, train B will catch up to train A at 9:07 p.m.