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anonymous

  • one year ago

Yoohoo, hey, I have another ridiculously complicated problem that has two parts to it. Here's a chance to get two medals, btw To get to school from home, Lana has to cycle one mile up a hill and one mile down the other side. She averages 10mph on the way up the hill. Part the first: What constant speed must Lana go down the hill if she wishes to average 12mph for the whole journey? Part the second: Explain why it's impossible for Lana to average 20mph for the entire journey. Thanks :)

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  1. anonymous
    • one year ago
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    yeah, this is basically a copy of the previous question, but something weird happened so yeah, teehee

  2. anonymous
    • one year ago
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    Since this is technically two questions, the person who answers this I will give a medal, and then post a new question: Hey (insert person's name) and mention the person, and then give a second medal.

  3. anonymous
    • one year ago
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    If you answer only one part, then I'll give you one medal, and the second person who answers will get a medal using the same method above. :)

  4. anonymous
    • one year ago
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    hmmm this is a tough one...

  5. anonymous
    • one year ago
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    |dw:1444613381341:dw|

  6. anonymous
    • one year ago
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    okay

  7. jim_thompson5910
    • one year ago
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    Uphill: `Lana has to cycle one mile up a hill` and `She averages 10mph on the way up the hill` distance = 1 mile speed = 10 mph D = r*t 1 = 10*t 1/10 = t 0.1 = t t = 0.1 so it takes 0.1 hrs to go up the hill ------------------------------------------------------- Downhill let x = speed going downhill "one mile down the other side", so D = 1 D = r*t 1 = x*t 1/x = t t = 1/x It takes her 1/x hours to go down the hill ------------------------------------------------------- Total distance: (distance uphill) + (distance downhill) = 1+1 = 2 miles D = 2 Total Time: 0.1+1/x hours T = 0.1 + 1/x We want the average speed to be 12 mph. So r = 12 D = r*t 2 = 12*(0.1+1/x) 2 = 1.2 + 12/x 2 - 1.2 = 12/x 0.8 = 12/x 0.8x = 12 x = 12/0.8 x = 15 So she must go 15 mph down the hill to average 12 mph overall (for the entire journey uphill and downhill)

  8. anonymous
    • one year ago
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    oh okay thanks

  9. anonymous
    • one year ago
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    hey people, you guys still have a chance, theres still a second medal out there waiting for an answer to come claim it

  10. anonymous
    • one year ago
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    and Jim-san, you are wonderful, your answers are so thorough and clear

  11. jim_thompson5910
    • one year ago
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    Part 2) ` Explain why it's impossible for Lana to average 20mph for the entire journey. ` The total distance is still 2 miles. So D = 2 The total time is still t = 1+1/x The only thing that's different is that we want the overall speed to be r = 20 now (instead of r = 12) D = r*t 2 = 20*(0.1+1/x) 2 = 2+20/x 2-2 = 20/x 0 = 20/x 0*x = 20 0 = 20 ... this equation is always false since the last equation is false, this means that `2 = 20*(0.1+1/x)` is false for any value of x. There are no numbers we can replace x with to make `2 = 20*(0.1+1/x)` true. So that's why it's impossible to make the overall speed 20 mph

  12. jim_thompson5910
    • one year ago
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    sorry I meant to say `The total time is still t = 0.1+1/x` I changed the `1` to `0.1`

  13. anonymous
    • one year ago
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    ok

  14. anonymous
    • one year ago
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    oh part two ok

  15. anonymous
    • one year ago
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    let me just finish jotting the rest down and then I'll give u the next medal :)

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