Trains A and B are traveling in the same direction on perallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 2:10 A.M. if train B passes the same station at 2:22 A.M, at what time will train B catch up to train A?

Question

Trains A and B are traveling in the same direction on perallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 2:10 A.M. if train B passes the same station at 2:22 A.M, at what time will train B catch up to train A?

Answer 1

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Answer 3

To determine the time at which train B catches up to train A, we need to calculate the time difference between when train A passes the station and when train B passes the same station.

First, let's find out the time difference between 2:10 A.M. (when train A passes the station) and 2:22 A.M. (when train B passes the station).

The time difference is 12 minutes (22 - 10 = 12).

Now, let's determine the distance that train A travels during this time difference. Since both trains are traveling in the same direction, the distance between them is equal to the relative speed between the two trains.

The relative speed of train B with respect to train A is calculated by subtracting the speed of train A from the speed of train B: 120 mph - 100 mph = 20 mph.

Therefore, train B is gaining on train A at a rate of 20 miles per hour.

To determine the distance train A travels during the 12-minute time difference, we can use the formula:

Distance = Speed * Time

The time difference needs to be converted from minutes to hours. There are 60 minutes in an hour, so 12 minutes is equal to 12/60 = 0.2 hours.

Distance = 100 mph * 0.2 hours = 20 miles

So, train A travels 20 miles during the 12-minute time difference.

Now, we can find out how long it will take for train B to catch up to train A.

To calculate the time, we'll use the formula:

Time = Distance / Relative Speed

Time = 20 miles / 20 mph = 1 hour.

Therefore, train B will catch up to train A in 1 hour.

To determine the time at which train B catches up to train A, we add this 1-hour to the time train A passed the station, which was 2:10 A.M.

2:10 A.M. + 1 hour = 3:10 A.M.

So, train B will catch up to train A at 3:10 A.M.