Trains a and b are travelling in the same direction on parallel tracks. Train a is travelling at 40mph and train b is travelling 48mph.Train a passes a station at 3:10 a.m. If train b passes the same station at 3:40 a.m., at what time willtrain b catcth up tomtrain a?
Remember your formula d=rt
40t=48(t-.30)
40t=48t-14.4
combine like terms
40t-48t=-14.4
8t=-14.4
isolate your t
t= 14.4/8 or 1.8 hours
With these word problems it is important to have your formula chart handy. This gives you a map to finding the answer.
To find out at what time train b will catch up to train a, we need to calculate the time it takes for train b to catch up to train a after train b passes the station.
First, let's find the time difference between when train b passes the station (3:40 a.m.) and when train a passes the station (3:10 a.m.). The time difference is 30 minutes.
Now, we need to determine the distance that train a travels during this time. Since train a is traveling at a constant speed of 40 mph, we can calculate the distance using the formula distance = speed × time. In this case, distance = 40 mph × 30/60 hours (since 30 minutes is half an hour). So, the distance covered by train a in this time is 20 miles.
Now, we know that train b needs to cover this distance in order to catch up to train a. The relative speed between train a and train b is the difference in their speeds, which is 48 mph - 40 mph = 8 mph.
Using the formula distance = speed × time again, we can calculate the time it will take for train b to cover a distance of 20 miles at a speed of 8 mph. So, time = distance ÷ speed = 20 miles ÷ 8 mph = 2.5 hours.
Finally, to determine the time when train b will catch up to train a, we add the time it took for train b to catch up (2.5 hours) to the time when train b passed the station (3:40 a.m.). Adding 2.5 hours to 3:40 a.m. gives us 6:10 a.m.
Therefore, train b will catch up to train a at 6:10 a.m.