SOLUTION: A train leaves toronto to Montreal travelling (60km)/(h ) a second train leaves toronto heading for Montreal half an hour later at (75km)/(h) how long will it take for the second t

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Question 1158063: A train leaves toronto to Montreal travelling (60km)/(h ) a second train leaves toronto heading for Montreal half an hour later at (75km)/(h) how long will it take for the second train to catch up to the first train?
Found 3 solutions by josmiceli, greenestamps, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The head start of the 1st train is:
+d%5B1%5D+=+60%2A%281%2F2%29+
+d%5B1%5D+=+30+ km
Let +d+ = the distance the 2nd train travels
until it catches the 1st train
Let +t+ = time in hrs for the 2nd train to
catch the 1st train
Start a stopwatch hen the 2nd train leaves
----------------------------
Equation for the 1st train:
(1) +d+-+d%5B1%5D+=+60t+
Equation for the 2nd train:
(2) +d+=+75t+
-------------------------------
(1) +d+-+30+=+60t+
Plug (2) into (1)
(1) +75t+-+30+=+60t+
(1) +15t+=+30+
(1) +t+=+2+
It takes 2 hrs for the 2nd train to catch the 1st train
--------------------------------
check:
(2) +d+=+75t+
(2) +d+=+75%2A2+
(2) +d+=+150+ km
and
(1) +d+-+d%5B1%5D+=+60t+
(1) +d+-+30+=+60%2A2+
(1) +d+=+30+%2B+120+
(1) +d+=+150+ km
OK

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


In the half hour before the second train starts, the first train travels (60)(1/2) = 30 km.

The second train catches up to the first train at a rate of (75-60)=15km/hr.

The number of hours it takes the second train to catch up to the first is 30/15 = 2.

ANSWER< 2 hours

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A train leaves toronto to Montreal travelling (60km)/(h ) a second train leaves toronto heading for Montreal half an hour later at (75km)/(h) how long will it take for the second train to catch up to the first train?
Let time second train takes to catch up to 1st train be T

Then the 1st train had traveled for "T + l" hours before the second train caught up to it

We then get the following DISTANCE equation: matrix%281%2C3%2C+60%28T+%2B+1%2F2%29%2C+%22=%22%2C+75T%29

60T + 30 = 75T

30 = 75T - 60T

30 = 15T

Time second train took to catch up to 1st train, or highlight_green%28matrix%281%2C6%2C+T%2C+%22=%22%2C+30%2F15%2C+%22=%22%2C+2%2C+hours%29%29