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

- chestercat

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- anonymous

yeah, this is basically a copy of the previous question, but something weird happened so yeah, teehee

- anonymous

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.

- anonymous

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. :)

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## More answers

- anonymous

hmmm this is a tough one...

- anonymous

|dw:1444613381341:dw|

- anonymous

okay

- jim_thompson5910

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)

- anonymous

oh okay thanks

- anonymous

hey people, you guys still have a chance, theres still a second medal out there waiting for an answer to come claim it

- anonymous

and Jim-san, you are wonderful, your answers are so thorough and clear

- jim_thompson5910

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

- jim_thompson5910

sorry I meant to say `The total time is still t = 0.1+1/x`
I changed the `1` to `0.1`

- anonymous

ok

- anonymous

oh part two ok

- anonymous

let me just finish jotting the rest down and then I'll give u the next medal :)

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