SOLUTION: Two trains are traveling between city A and city B on parallel tracks. The first train will leave at 10:30 AM traveling at a velocity if 35 mph toward city B. The second train will

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Question 601729: Two trains are traveling between city A and city B on parallel tracks. The first train will leave at 10:30 AM traveling at a velocity if 35 mph toward city B. The second train will leave city B at 2:30 PM traveling at a velocity of 60 mph toward city A. The two cities are 350 miles apart.
Write the parametric equations that describe this situation.
How long does each train travel before they pass eachother?
Which train will reach its destination first?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Two trains are traveling between city A and city B on parallel tracks.
The first train will leave at 10:30 AM traveling at a velocity if 35 mph toward city B.
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1st train DATA:
rate = 35 mph ; time = x hrs ; distance = 35x miles
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The second train will leave city B at 2:30 PM traveling at a velocity of 60 mph toward city A.
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2nd train DATA:
rate = 60 mph ; time = x-4 hrs ; distance = 60(x-4) miles
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The two cities are 350 miles apart.
Write the parametric equations that describe this situation.
How long does each train travel before they pass each other?
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Equation:
distance + distance = 350
35x + 60(x-4) = 350
35x + 60x - 240 = 350
95x = 590
x = 6.21 hrs. = 6 hr 12 minutes
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Which train will reach its destination first?
Train A takes 350/35 = 10 hrs
10 hrs from 10:30AM is 8:30 PM
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Train B takes 350/60 = 5.83 hrs = 5 hr + 50 minutes
5.83 hrs from 2:30 PM is 8:20 PM
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Train B will get to A before train A gets to B.
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Cheers,
Stan H.