Question 179888: I am really stuck on this problem and could use some help.
At noon a train leaves Los Angeles, headed for Las Vegas, a distance of 260 miles. The train travels at a speed of 60 mph. At 1p.m. a second train leaves Las Vegas headed for Los Angeles, traveling at 40 mph. How long after the train leaves Las Vegas will the two trains pass each other?
This is how I attempted to work it out:
1st train distance= 60(x+1), rate= 60mph, time= x+1
2nd train distance= 40x, rate=40mph, time=x
60(x+1)=40x
60x +60=40x
60 =-20x
-3 =x
The trains could not pass at -3 hours. I can't figure out what I'm doing wrong! Please help. :-)
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! well one easy way to do this problem based on them traveling at 100mph together
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so if total distance is 260 miles. after 1 hour the trains are only 200 miles apart when train #2 starts moving
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if they are traveling 100mph together then they will cover that 200 miles in 2hours.
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so the answer is 2 hours
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lets use your figures:
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1st train distance= 60(x+1), rate= 60mph, time= x+1
2nd train distance= 40x, rate=40mph, time=x
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distances will not be equal. distance for train 2 lets call d and for train 1 lets call distance 260-d
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260-d=60(x+1).....eq 1
d=40x.............eq 2
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plug d's value from eq 2 into eq 1
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260-40x=60x+60
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200=100x
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x=2
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so really the only mistake you made was to set the distances equal to each other...good job
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