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anonymous

  • 5 years ago

A car travels 382 miles in 8 hours. The first part of the trip, through the mountains, the car's speed is 42mph, and the second part the car's speed is 58mph. It took ? hours the first part of the trip. Round to the nearest tenth. I need someone to explain a solution to finding the answer to this problem. And please explain every step of your solution to the end, and why you are doing your solution the way you are doing it.

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  1. mathteacher1729
    • 5 years ago
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    Let's change the numbers but keep the idea the same. A car travels 200 miles in 4 hours. It was going 65mph for the first part of the trip, and 85mph for the 2nd part of the trip. How long was each part of the trip? The key here is to set up a system of equations: "65 mph for x hours plus 85 mph for y hours means we've traveled 382 miles." 65x + 85y = 382 "the time spent driving was 4 hours" x+y = 4 Can you see what to do next?

  2. anonymous
    • 5 years ago
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    Let time take for the first part of the trip = x Distance traveled for first part of the trip = 42 * (x) Distance traveled for the second part of the trip = 58 * (8-x) Sum of the distance = 382 So 42x + 58(8-x) = 382 Solve for x

  3. anonymous
    • 5 years ago
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    Formula used: Distance = Speed x Time

  4. anonymous
    • 5 years ago
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    jgeorge, I know the formula, just can't see how it applied to this problem. Where did you get the 8-x in your equation?

  5. anonymous
    • 5 years ago
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    total time taken = 8 hours time taken for the first half = x so time taken for the second half = total time - time taken for the first half = 8 - x Is that okay?

  6. mathteacher1729
    • 5 years ago
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    indiana -- did my answer help?

  7. anonymous
    • 5 years ago
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    mathteacher...your answer did help some...I did not think of using 2 different variables in the equation, for each leg of the journey...

  8. anonymous
    • 5 years ago
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    But I guess I was looking more for an equation that used the same variable, which is how jgeorge did it, and it makes more sense to me.

  9. anonymous
    • 5 years ago
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    A negative number divided by a negative number equals a positive number, right?

  10. anonymous
    • 5 years ago
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    Yep

  11. mathteacher1729
    • 5 years ago
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    Cool, whichever method works best for you -- go for it! :D

  12. anonymous
    • 5 years ago
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    Thanks jgeorge...mathteacher1729....I will be using this sight extensively...I'm majoring in nursing. :)

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