The shuttle service has a train going from Washington to NY City and from NY City to Washington every hour on the hour. The trip from one city to the other takes 4 1/2 hours, and all trains travel at the same speed. How many trains will you pass in going from Washington to NY City? Thanks for help.
+37084 Let's say you are on the 10:00 train .... you will see the train coming form the opposite direction that was launched at 6:00 after you have been traveling approx 30 minutes ...
then t you will see the 7 8 9 10 launches as you travel for 4 1/2 hours AND you will see the 11 12 13:00 and 14:00 train launches before you arrive at the launching station at 14:30
That is a total of 9 trains going the opposit direction as you ....
+37084 Let's say you are on the 10:00 train .... you will see the train coming form the opposite direction that was launched at 6:00 after you have been traveling approx 30 minutes ...
then t you will see the 7 8 9 10 launches as you travel for 4 1/2 hours AND you will see the 11 12 13:00 and 14:00 train launches before you arrive at the launching station at 14:30
That is a total of 9 trains going the opposit direction as you ....
As our train leaves Washington, there is a train just 1 hour away from Washington, another 2 hours away...etc. Since the trains are traveling at the same rate of speed, we will pass the train that is 1 hour away from Washington in 1/2 hour, the train 2 hours away in 1 hour, or 1/2 hour after passing the preceding train. That is, we pass a train every 1/2 hour. Since the trip takes 4 1/2 hours or 9 half-hours, and as we leave Washington, we also pass a train just arriving. We, therefore, will pass a total of 10 trains during our trip!!.
+129840 Suppose our train left the station at 12 midnight. [every hour on the hour]....we would meet no train at that time because the other train would have had to have left at 7:30AM the previuos evening....but this is impossible because it would not have left "on the hour"
Instead, 15 minutes later [ at 12:15 AM].....we have met the train the left the other station at 8AM the previous evening [ and would arrive at our station of departure 15 minutes later....at 12:30 AM ]
Then......30 minutes later [ at 12:45 AM] we would meet the train that left at 9 AM the previous evening.......it has been traveling for 3 hrs, 45 min....and since we are 45 minutes from our station of departure......it's 45 min from its station of arrival......and it will arrive at 1:30 AM.....4 1/2 hours after its departure
Note the remaining patterns :
Our Time → Time that the train we meet left the station of departure [our station of arrival ]
1:15 AM → 10 PM
1:45 AM → 11AM
2:15 AM → 12 AM
2:45 AM → 1 AM
3:15 AM → 2 AM
3:45 AM → 3 AM
4:15 AM → 4 AM
Note that we don't meet any more trains after 4:15 AM.......we arrive at the station at 4:30AM, but the next train that departs that staion won't happen for 30 more minutes [ at 5 AM]
So....we pass a total of 9 trains......
