I have tried this several different ways and I am just not satisfied with the answer I keep coming up with.
Trains A and B are traveling at the same direction on parallel tracks. Train A is traveling at 100 mph and train B is traveling at 120 mph. Train A passes a station at 4:10 pm. If train B passes the same station at 4:22 pm, at what time will train B catch up with train A?
Trains A and B are traveling at the same direction on parallel tracks. Train A is traveling at 100 mph and train B is traveling at 120 mph. Train A passes a station at 4:10 pm. If train B passes the same station at 4:22 pm, at what time will train B catch up with train A?
Something is wrong here. If train B is traveling 20 mph faster than A, B should reach the station first. Unless they are traveling on a circular track, B will never "catch up" to A. B is going faster.
Please repost with accurate data. Thanks for asking.
This is verbatum, and that is why I am having problems with it myself.
Discuss it with your teacher or whomever gave you the problem.
Sorry I can't help you more.
There is nothing worng with the problem.
When A passes the station B is some distance behind (we don't know how far - we don't care)
When B passes the station A is some distance in front, the distance (Na) being
Na=12(100)/60 miles.
Nb=0 miles
The trains now continue in the same direction.
after time tx the distances are now
Na = 12(100)/60 + tx(100)/60
Nb= tx(120)/60
which are equal when Na=Nb
so
12(100)/60 + tx(100)/60 = tx(120)/60
1200 +100tx = 120tx
1200 = 20tx so Tx=60
So B catches up with A at 5:22, i.e. 60 minutes after B passes the station.
But check my working
The problem does not say the trains started out at the same time so even though B is travelin faster it could still be behind A
To find out at what time train B will catch up with train A, we can use the concept of relative speed.
First, let's determine the time difference between train A passing the station and train B passing the station. Since train A passed the station at 4:10 pm and train B passed it at 4:22 pm, the time difference is 12 minutes or 12/60 = 0.2 hours.
Now, let's calculate the distance between train A and train B when train B passes the station. We know that train A has already been traveling for 0.2 hours longer than train B. The distance train A has covered during this time is 0.2 hours * 100 mph = 20 miles.
The relative speed between train A and train B is the difference in their speeds. In this case, the relative speed is 120 mph - 100 mph = 20 mph.
Since train A has a head start of 20 miles and train B's relative speed to train A is 20 mph, train B will catch up to train A in 20 miles / 20 mph = 1 hour.
Therefore, train B will catch up with train A at 4:22 pm + 1 hour = 5:22 pm.
So, the answer is train B will catch up with train A at 5:22 pm.