Trains a and b are traveling in the same direction on parallel tracks;Train a is traveling 40mph and train b is traveling 50mph. Train A passes a station at 8:15 am. If train b passes the same station at 8:27 am what time will train b catch up to train a?
I know this is a distant rate a time question but cannot seem to write out the correct formula and arrive at a correct answer.
The distance between the trains decreases at a rate of 50 - 40 = 10 mph = 1/6 mile per minute.
At 8:27 PM, train A is (1/6 h) * 40 miles/h = 40/6 miles ahead of B.
The 40/6 mile gap between trains will become zero after
t = (40/6 mile)/(1/6 mile/minute)
= 40 minutes
so they will meet up at 9:07 am?
Yes
To solve this problem, we can use the formula: Time = Distance / Speed.
First, let's find the time it takes for train A to reach the station. Since train A passes the station at 8:15 am, let's assume it takes t hours for train A to reach the station.
Distance traveled by train A = Speed of train A × Time taken by train A
Distance traveled by train A = 40 mph × t
Next, let's find the time it takes for train B to reach the station. Since train B passes the same station at 8:27 am, it means that train B takes 12 minutes less than train A to reach the station. Therefore, it takes t - 12/60 hours for train B to reach the station.
Distance traveled by train B = Speed of train B × Time taken by train B
Distance traveled by train B = 50 mph × (t - 12/60)
Since train B will catch up to train A when both trains are at the same distance from the station, we can set the two distances traveled equal to each other:
40 mph × t = 50 mph × (t - 12/60)
Now, we can solve for t to find the time at which train B catches up to train A:
t = (50/40) × (t - 12/60)
Simplifying the equation:
40 × 50 × t = 50 × 40 × (t - 12/60)
2000t = 2000t - 800
800 = 0t
Since the equation 800 = 0 does not have any solutions, it means that train B will never catch up to train A in this scenario. It is not possible for train B to catch up to train A.