trains A and B are traveling in the same direction on paraleel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 88 miles per hour. Train a passes a station at 5:10 P.M. If train B passes the same station at 5:40 P.M., at what time will train B catch up to train A?
Consider t=0 when train A passes the station. After that, at some time t, the trains will be at the same distance. B travels 0.5 hour less than A.
88(t-.5) = 80t
88t - 44 = 80t
8t = 44
t = 5.5
So, 5.5 hours after 5:10, the trains will have gone the same distance (440 miles) from the station.
That is, at 10:40, B passes A.
To find the time when train B catches up to train A, we first need to determine the time difference between when train A passes the station and when train B passes the station.
We know that train A passes the station at 5:10 P.M., so the time it takes for train A to reach that point is already known.
Next, we need to find the distance that train B travels in that time. To do this, we can use the formula: distance = speed × time.
The difference in time between when train A passes the station and when train B passes the station is 30 minutes or 0.5 hours (since there are 60 minutes in an hour).
Using the formula, we can calculate the distance traveled by train B during this time as follows:
distance = speed × time
distance = 88 mph × 0.5 h
distance = 44 miles
So, train B catches up to train A after traveling a distance of 44 miles.
Now, we need to determine the additional time it takes for train B to cover this distance at its faster speed compared to train A.
To find this time, we can use the formula: time = distance / speed. Plugging in the values, we have:
time = 44 miles / (88 mph - 80 mph)
time = 44 miles / 8 mph
time = 5.5 hours
Therefore, train B will catch up to train A 5.5 hours after train A passes the station.
To know the exact time for this, we add 5.5 hours to the time when train A passed the station (5:10 P.M.):
5:10 P.M. + 5.5 hours = 10:40 P.M.
So, train B will catch up to train A at 10:40 P.M.