SOLUTION: Hi. I continually have difficulty solving distance problems involving multiple variables. Here is my question. Thank you so much.
A railroad and a highway intersect at right an
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-> SOLUTION: Hi. I continually have difficulty solving distance problems involving multiple variables. Here is my question. Thank you so much.
A railroad and a highway intersect at right an
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Question 715206: Hi. I continually have difficulty solving distance problems involving multiple variables. Here is my question. Thank you so much.
A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart?
There are two answers:
First time = _______ minutes
Second time = ______ minutes Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart?
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Draw the picture so you can see what is happening with the distances:
Train DATA:
rate = 30 mph ; time = t hours ; distance = 30t miles
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Car DATA:
rate = 30 mph ; time = t hour ; distance = 30t miles
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Distance train is from the intersection: 10-30t miles
Distance car is from the intersection: 6-30t miles
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Use Pythagoras:
(10-30t)^2 + (6-30t)^2 = 4^2
100 - 600t + 900t^2 + 36 - 360t + 900t^2 = 16
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1800t^2 -960t + 120 = 0
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Divide thru by 120 to get:
15t^2 - 8t + 1 = 0
(3t-1)(5t-1) = 0
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t = 1/3 hr = 20 min
Or
t = 1/5 hr = 12 min
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Cheers,
Stan H.
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