SOLUTION: two cars leave from same location and travel the opposite directions along a road. One car travels 30 mph while the other travels at 45 mph. How long will it take the two cars to b

Question 460773: two cars leave from same location and travel the opposite directions along a road. One car travels 30 mph while the other travels at 45 mph. How long will it take the two cars to be at 255 miles apart? thank you!
Found 2 solutions by robertb, bucky:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Do the two cars leave the same location AT THE SAME TIME? Or some time apart?

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Since the cars are traveling in opposite directions, their distances can be added to find the distance between them. For example, how far apart are they in 1 hour? In one hour the car that is going 30 mph will have gone 30 miles (Distance = Rate * Time = 30 * 1). In that same hour the car that is going 45 mph will have gone 45 miles (Distance = Rate * Time = 45 * 1). So in one hour the total distance between the cars is the sum of these two or 30 + 45 = 75 miles.
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Using that same method you can say that the total distance between the cars is the sum of the two distances of each car. Since the distance traveled by each car is given by its rate (R) times the time it has been going (T) then in time T the first car goes a distance:
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In the same way, the second car goes a distance:
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So that the total distance between the cars is the sum:
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And the problem states that this total distance equals 255 miles. Therefore, you can write the equation:
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Add the two terms on the left side to get:
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Divide both sides by 75 to solve for T:
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Perform the division:
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So in 3.4 hours the two cars are 255 miles apart.
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You can put the answer into a form that is more familiar to most people by realizing that an hour is 60 minutes so that each tenth of an hour is 6 minutes. Therefore, 4 tenths of an hour is 4 times 6 minutes or 24 minutes. And 3.4 hours is 3 hours and 24 minutes.
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Therefore, the two cars are 255 miles apart in 3 hours and 24 minutes.
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Hope this helps you to understand the problem and how to understand better any problems that involve Distance = Rate times Time.
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