Question 85559: Two cars leave Dallas; one is traveling south on I-45 at 65 mph. The other travels north at 70 mph. They are talking to each other on walkie talkies. They can only talk to each other if they are within 20 miles of each other. How long will it be before the cars are 20 miles apart?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Use the equation:
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Distance = Rate * Time
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And apply it to each car. Time will be in hours and Rate will be in mph. Therefore,
the Distance will be in miles.
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Since the cars are headed in opposite directions, the distance between them will be the
sum of the distance that each car travels.
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The distance (call it D1) that the first car travels is its Rate (65 mph) times the Time
it travels. In equation form this can be written as:
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D1 = 65*T
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The distance that the second car travels (D2) is its Rate (70 mph) times the time that it
travels. Since it starts out at the same time that the first car did, it travels the
same amount of time that the first car does. In equation form this is:
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D2 = 70*T
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The sum of the two distances is to be 20 miles, because we want to solve for the time that
they reach that separation so we know how long before they lose contact with each other.
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So we write:
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D1 + D2 = 20 = 65*T + 70*T
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We can add 65*T to 70*T and the equation then becomes:
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20 = 135*T
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To solve for T just divide both sides of this equation by 135 and you get:
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T = 20/135 = 0.148148148 hours.
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That is the amount of time before the two cars are 20 miles apart.
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Since an hour contains 60 minutes, we can multiply 60 by 0.148148148 and find that they
will only be able to communicate with each other for 8.888888 minutes. Not very much time
to talk.
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Hope this helps you to understand the problem a little better.
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