Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 mile per hour and train B is traveling at 88 miles per hour. Train A passes a station at 9:20 P.M. If train B passes the same station at 9:50 P.M., at what time will train B catch up with train A?
To determine the time when Train B catches up with Train A, we need to find the time difference between their passage at the station. Train B passes the station 30 minutes after Train A did.
Given that Train A is traveling at 80 miles per hour and Train B is traveling at 88 miles per hour, the relative speed between them is the difference in their speeds, which is 88 - 80 = 8 miles per hour.
Since Train B catches up with Train A at a rate of 8 miles per hour, we can set up a simple equation to find the time it takes for Train B to catch up:
Distance = Speed × Time
Let's represent the time for Train B to catch up as 'T'.
The distance traveled by Train B in T hours is equal to the distance traveled by Train A in (T + 0.5) hours (0.5 hours = 30 minutes).
So, we have the equation:
88T = 80(T + 0.5)
Now we can solve for 'T'.
88T = 80T + 40
88T - 80T = 40
8T = 40
T = 40/8
T = 5 hours
Therefore, Train B will catch up with Train A after 5 hours.
To find the exact time, we need to add the catching up time (5 hours) to Train B's initial passing time (9:50 PM).
9:50 PM + 5 hours = 2:50 AM (next day)
So, Train B will catch up with Train A at 2:50 AM.
let the time be t hrs after train B passes the station.
At that moment train A will be 40 miles down the track (1/2 hour x 80 mph)
and will travel another 80t miles
when train B reaches train A, train B will have traveled 88t miles
so 88t = 40 + 80t
solve for t
add t to 9:50 pm