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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 :)
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, this is basically a copy of the previous question, but something weird happened so yeah, teehee

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Since 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If 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. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm this is a tough one...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444613381341:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5Uphill: `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)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hey people, you guys still have a chance, theres still a second medal out there waiting for an answer to come claim it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and Jimsan, you are wonderful, your answers are so thorough and clear

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5Part 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 22 = 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5sorry I meant to say `The total time is still t = 0.1+1/x` I changed the `1` to `0.1`

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me just finish jotting the rest down and then I'll give u the next medal :)
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