anonymous
  • anonymous
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.
Mathematics
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SOLVED
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katieb
  • katieb
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mathteacher1729
  • mathteacher1729
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?
anonymous
  • anonymous
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
anonymous
  • anonymous
Formula used: Distance = Speed x Time

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anonymous
  • anonymous
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?
anonymous
  • anonymous
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?
mathteacher1729
  • mathteacher1729
indiana -- did my answer help?
anonymous
  • anonymous
mathteacher...your answer did help some...I did not think of using 2 different variables in the equation, for each leg of the journey...
anonymous
  • anonymous
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.
anonymous
  • anonymous
A negative number divided by a negative number equals a positive number, right?
anonymous
  • anonymous
Yep
mathteacher1729
  • mathteacher1729
Cool, whichever method works best for you -- go for it! :D
anonymous
  • anonymous
Thanks jgeorge...mathteacher1729....I will be using this sight extensively...I'm majoring in nursing. :)

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