train A and B are traveling in the same direction on parallel tracks. train A is going 80 miles per hour train B is going 84 miles per hour. train A past a station at 2:15 am train B passes at 2:45 am what time will train B catch train A
In order to catchup, train B must travel the same distance; but its' time must be 1/2 hour less:
Train A time = t hrs,
Train B time = (t - 0.5) hrs.
d2 = d1,
84(t - 0.5) = 80t,
84t - 42 = 80t,
84t - 80t = 42,
4t = 42,
t = 42/4 = 10.5 hrs,
(t - 0.5) = 10.5 - 0.5 =10h to catchup.
To determine the time when Train B will catch up to Train A, we need to compare the distance covered by both trains.
First, let's find out the time difference between when Train A passed the station (2:15 am) and when Train B passed the station (2:45 am). The time difference is 30 minutes or half an hour.
Next, we calculate the distance that Train A traveled during this 30-minute time difference. Given that Train A is moving at a speed of 80 miles per hour, we can use the formula speed = distance/time to find the distance covered by Train A:
Distance covered by Train A = 80 mph * (30 min / 60 min / hour) = 40 miles.
Now, we know that Train B is moving faster than Train A. The speed difference between them is 84 mph - 80 mph = 4 miles per hour.
Since Train B needs to cover the distance of 40 miles that Train A gained during the 30-minute time difference, we can calculate the time it will take for Train B to catch up by dividing this distance by the speed difference:
Time = Distance / Speed = 40 miles / 4 mph = 10 hours.
Lastly, we need to add this time to the time when Train B passed the station (2:45 am) to determine the time when Train B will catch up with Train A:
2:45 am + 10 hours = 12:45 pm (noon).
Therefore, Train B will catch up to Train A at 12:45 pm.