A quick question to check my answer.
Trains A & B are travelling in the same direction on parallel tracks. Train A is travelling at 100 miles per hour and train B is travelling at 110 miles per hour. Train A passes a station at 2:10 A.M. If train B passes the same station at 2:40 A.M., at what time will train B catch up to train A?
My answer is 7:40 A.M.
Here is my reasoning:
Train A is ahead of Train B by 30 minutes.
This means that by the time train B gets to the station, train A would have travelled 50 miles.
So every hour that Train A travels, Train B closes the gap because it is 10 miles an hour faster.
If I start their time at 2:40 A.M., here is what I come up with:
Time/Train-A/Train-B
2:40/50/0
3:40/150/110
4:40/250/220
5:40/350/330
6:40/450/440
7:40/550/550 <-- Both trains would have travelled the same distance by 7:40.
Can someone double check. Thanks.
your answer is correct
an easier way is the following:
let the time past 2:10 be t hours
so when they pass each other , the slower train has gone for t hours and the faster train for 1-1/2 hrs.
so 110(t-1/2) = 100t
10 t = 55
t = 5.5 hrs or 5 hours and 30 min
add that to 2:10 to get 7:40
Your reasoning is correct, and your answer of 7:40 A.M. is also correct. You have correctly calculated that Train A is ahead of Train B by 50 miles when Train B passes the station at 2:40 A.M.
Since Train B is traveling at a faster speed than Train A, it will gradually close the gap between them. And as you have correctly observed, for every hour that Train A travels, Train B closes the gap by 10 miles.
Using this logic, you have calculated the distances traveled by both trains at each hour interval:
- At 3:40 A.M., Train A would have traveled 100 miles, while Train B would have traveled 110 miles, closing the gap to 150 - 110 = 40 miles.
- At 4:40 A.M., Train A would have traveled 200 miles, while Train B would have traveled 220 miles, closing the gap to 250 - 220 = 30 miles.
- At 5:40 A.M., Train A would have traveled 300 miles, while Train B would have traveled 330 miles, closing the gap to 350 - 330 = 20 miles.
- At 6:40 A.M., Train A would have traveled 400 miles, while Train B would have traveled 440 miles, closing the gap to 450 - 440 = 10 miles.
Finally, at 7:40 A.M., Train A would have traveled 500 miles, while Train B would have traveled 550 miles. At this point, both trains would have traveled the same distance, and Train B would have caught up to Train A. Therefore, your answer of 7:40 A.M. is correct.