Question 683291: Two stations A and B on a railway line are 144 kilometers apart. A fast train starts from B at 9 a.m., another fast train travelling at the same speed starts from A at 10 a.m. A slow train starts from B at 10:20 a.m., the fast train from A meets the other fast train at 11:30 a.m., and the slow train at 12:32 p.m. When does the slow train reach A?
(Ans: At 4:20 p.m.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two stations A and B on a railway line are 144 kilometers apart.
A fast train starts from B at 9 a.m., another fast train traveling at the same speed starts from A at 10 a.m.
A slow train starts from B at 10:20 a.m., the fast train from A meets the other fast train at 11:30 a.m., and the slow train at 12:32 p.m.
When does the slow train reach A?
:
Use the fast train meeting to find the speeds of those trains
Let s = speed of the fast trains,
write distance equation: dist = speed * time
:
Change the times to hrs;
1.5 hrs travel time of train from A
2.5 hrs travel time of train from B
:
1.5s + 2.5s = 144 km
4s = 144
s = 144/4
s = 36 mph is the speed of the fast trains
:
When the train from A meets the slow train from B, find speed of slow train
Travel time of slow train to meeting point 2:12 which 2.2 hrs
travel time of fast train to meet slow train: 2:32 which is 2.533 hrs
:
let x = speed of the slow train
36*2.533 + 2.2x = 144
92.2 + 2.2x = 144
2.2x = 144 - 92.2
2.2x = 52.8
x = 52.8/2.2
x = 24 km/hr speed of the slow train
:
Find how long this train will take to go 144 km
144/24 = 6 hrs
slow train will arrive at A: 10:20 + 6 = 16:20 or 4:20 PM
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