I saw this posted but saw no help with it
Trains A & B are traveling in the same direction. Train A is traveling at 100 mph and Train B is traveling at 110mph Train A passes a station at 1:15 pm. If Train B passes the same station at 1:45 at what time will Train B catch up with Train A
To solve this problem, we need to determine the time it takes for Train B to catch up with Train A.
Now, since both trains are traveling in the same direction, Train B will catch up with Train A when the distance it covers is equal to the distance Train A has covered plus the distance between the two trains.
Since Train A passed the station at 1:15 pm, we can assume that Train B started chasing Train A at 1:45 pm (30 minutes later).
To find the time it takes for Train B to catch up, we need to compare the speeds of both trains.
Let's consider the relative speed of Train B with respect to Train A. The relative speed is calculated by subtracting the slower train's speed from the faster train's speed:
Relative speed = Speed of Train B - Speed of Train A
= 110 mph - 100 mph
= 10 mph
So, Train B is gaining on Train A at a rate of 10 miles per hour.
To determine the time it takes for Train B to catch up with Train A, we need to divide the distance between the two trains by the relative speed.
The distance between the two trains is the distance Train A covers in the time it takes Train B to catch up. Since the trains are traveling at constant speeds, we can use the formula:
Distance = Speed × Time
Let's represent the time it takes for Train B to catch up as "t" hours.
For Train A, distance = Speed of Train A × time
= 100 mph × t
For Train B, distance = Speed of Train B × time
= 110 mph × t
Now, we know that Train B starts chasing Train A 30 minutes (or 0.5 hours) after Train A passes the station.
So, the equation for the distance traveled by Train B is:
Distance of Train B = Speed of Train B × (t + 0.5)
Since Train A and Train B will cover the same distance when Train B catches up, we can set these two equations equal to each other:
100 mph × t = 110 mph × (t + 0.5)
Now, we can solve this equation to find the value of "t" which represents the time Train B catches up with Train A.
100t = 110(t + 0.5)
100t = 110t + 55
100t - 110t = 55
-10t = 55
t = -5.5
Since time cannot be negative in this context, we made an error somewhere in our calculations. Please double-check the information provided or the equation used for the calculation.