Theory's posts
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
What if the dodo brought the duck almost to the river but not quite, and the dodo went back to pick up the eaglet and the duck just stood there and waited until they returned so they could all cross together? It would still be 11 hours. So I don't think the "at the same time" really matters.
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
Okay...
Say the dodo takes the duck on the bike all the way to the end, meanwhile the eaglet begins on foot. Then the dodo rides back to pick the eaglet up.
In five hours, the dodo and duck reach the river. The eaglet has made it 75 km. The dodo begins riding back. There is a distance of 225 km between them now. After 3 hours, the dodo travels 60*3 = 180 km back, and the eaglet gets 15*3 = 45 km further. 180+45 = 225 so that's when they meet up. The dodo rides back with the eaglet in tow, that takes another 3 hours.
Total time is 5+3+3 = 11 hours. Is that the best we can do?
In five hours, the dodo and duck reach the river. The eaglet has made it 75 km. The dodo begins riding back. There is a distance of 225 km between them now. After 3 hours, the dodo travels 60*3 = 180 km back, and the eaglet gets 15*3 = 45 km further. 180+45 = 225 so that's when they meet up. The dodo rides back with the eaglet in tow, that takes another 3 hours.
Total time is 5+3+3 = 11 hours. Is that the best we can do?
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Littlewhitedragonlet: Ah yeah, I used to do that a lot too, take shortcuts in the algebra. Most of my teachers were able to read between the lines and figure it out (or they were lazy graders and didn't read it, haha). But once I started teaching, I started showing all my steps for the benefit of my students, and that's stuck with me. It feels more complete to show everything :)
Your work looks great to me though. I'd give you an A if were still teaching xD
Your work looks great to me though. I'd give you an A if were still teaching xD
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Littlewhitedragonlet: Having taught math, I can tell you that the reason we award no points for answers without work is because your work is how you show your thought process, and math is mostly logic, so we care way more about your thought process than we do a right or wrong answer.
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
I think I finally see what LittleWhiteDragonlet did!
Fast runner runs 3 laps by the time slow runner has run 1. I want to know where the slow runner gets lapped for the first time, and that'll be when the quick runner has run exactly one more lap than the slow runner. I get this system of equations:
q = 3s
q = s+1
So 3s = s+1
3s - s = 1
2s = 1
s = 1/2
So at 4 minutes, slow runner has run half a lap, or 200 m, and fast has run 1.5 laps, or 600 m.
4 minutes to run 600 m, how many minutes to run 3600? Here's that ratio:
600/4 = 3600/x
x = 24 minutes
q = 3s
q = s+1
So 3s = s+1
3s - s = 1
2s = 1
s = 1/2
So at 4 minutes, slow runner has run half a lap, or 200 m, and fast has run 1.5 laps, or 600 m.
4 minutes to run 600 m, how many minutes to run 3600? Here's that ratio:
600/4 = 3600/x
x = 24 minutes
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
Oh gosh, this looks tough.
The race begins at t = 0 minutes; quickest runner laps the slowest at t = 4 minutes.
The quick runner runs 3 times faster than the slow runner, so that means they get lapped again at t = 8, and t = 12, and so on until the fast runner finishes.
I'm thinking that the slow runner would be lapped three times, so the fast runner finishes in 12 minutes, but I'm not sure if this correct.
The quick runner runs 3 times faster than the slow runner, so that means they get lapped again at t = 8, and t = 12, and so on until the fast runner finishes.
I'm thinking that the slow runner would be lapped three times, so the fast runner finishes in 12 minutes, but I'm not sure if this correct.
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Shadami: Yeah, if the Rabbit leaves first and is faster than the Hare, then they'd never meet if they walked in a straight line forever.
So is it a trick question, and the answer is "never"?
So is it a trick question, and the answer is "never"?
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Shadami: gasp
I think that's right, I forgot the two hour time difference so it's 16+2
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Rainbowpanda: It's the hair, haha
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
Ugh I'm confusing myself.
Are we wrong?
The Rabbit is faster than the Hare so they won't meet along the way. They'll meet when the Hare gets there in 320/20 = 16 hours, as dragonlet said.
Are we wrong?
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
Oh god, are there three locations? There have to be, right? If there are only two, then they'd meet at the castle when the Hare gets there. But we don't know how far the Hole is from the Castle?
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Shadami: Hey, I won't knock trial and error! It's not the fastest way but it can definitely work xD
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Dipper: Well here's problem 2. I'm actually not bothering with the first one, all that counting looks way too tedious xD
4 large + 2 small takes the same amount of time as 2 large and 6 small
4L + 2S = 2L + 6S
4L - 2L = 6S - 2S
2L = 4S
L = 2S (A large brush can paint twice as much as a small. I'm gonna sub 2S in for L everywhere and convert all my large brushes to small so I have fewer variables)
4L + 2S = 10S
2L + 6S = 10S (we already knew it would be the same)
8L + 8S = 24S
It takes two hours to paint the garden with 10 small brushes. The more brushes we have, the less time it should take, so brushes and time have an inverse relationship. That means when I multiply or divide my brushes, I should do the opposite to my time.
10 brushes takes 120 minutes
10/10 brushes takes 120*10 min
1 brush takes 1200 min
1*24 brushes takes 1200/24 min
24 brushes takes 50 minutes to paint the whole garden
We wanted only half the garden though, so it would take half the time, or 25 minutes.
4L + 2S = 2L + 6S
4L - 2L = 6S - 2S
2L = 4S
L = 2S (A large brush can paint twice as much as a small. I'm gonna sub 2S in for L everywhere and convert all my large brushes to small so I have fewer variables)
4L + 2S = 10S
2L + 6S = 10S (we already knew it would be the same)
8L + 8S = 24S
It takes two hours to paint the garden with 10 small brushes. The more brushes we have, the less time it should take, so brushes and time have an inverse relationship. That means when I multiply or divide my brushes, I should do the opposite to my time.
10 brushes takes 120 minutes
10/10 brushes takes 120*10 min
1 brush takes 1200 min
1*24 brushes takes 1200/24 min
24 brushes takes 50 minutes to paint the whole garden
We wanted only half the garden though, so it would take half the time, or 25 minutes.
Posted in Ch. 3 White Rabbit's Watch
Posted 7 years ago
@Dipper: Nah, you're right. I'm still solving the ones I missed, so I get it :P