Knightmare's Empty Refrigerator
Knightmare got off the couch and went to the refrigerator to replenish his snack tray. OH NO! The beer supply was depleted and there was no dip for chips. He grabbed the car keys and went outside. He had forgotten that Chris had borrowed his vehicle to attend the Tiddly Wink championships in Puzzletown. He decided to walk to the store at the top of the long hill.
He walked up the hill at a rate of one and a half miles per hour. On the trip back home, he walked down the hill at four and a half miles per hour. It took him six hours to make the round trip.
How far was it to the top of the hill?
... and how many of you believe Knightmare walked for six hours? :)
He walked up the hill at a rate of one and a half miles per hour. On the trip back home, he walked down the hill at four and a half miles per hour. It took him six hours to make the round trip.
How far was it to the top of the hill?
... and how many of you believe Knightmare walked for six hours? :)
posted by Zaux at
9:22 PM
7 Comments:
t1+t2=6
d=1.5*t1
d=4.5*(6-t1)
1.5*t1=4.5*(6-t1)
t1=3*(6-t1)
4t1=18
t1=18/4
t1=4.5
t2=6-t1=1.5
d=4.5*1.5=6.75
Answer:
6.75 miles, and I think the probability of the walk is ~= lim 1/x as x-> inf.
But Pequod may have done it.
Cam
well, certainly you're right...
Cam, do you figure out how to post puzles?
Not as concise as Cam's method, but here's mine:
walked up hill @ 3/2 mph
walked downhill @ 9/2 mph
total time = 6 hrs.
time up = x
time down = 6-x
du = distance up
dd = distance down
du = dd
du = 3/2 mph * x
dd = 9/2 mph * (6-x)
3/2 mph * x = 9/2 mph * (6-x)
3x/2 = (54-9x)/2
3x = 54 - 9x
12x = 54
x = 4 1/2 hours uphill
9/2 hrs. * 3/2 mph = du = dd
27/4 miles = d
d = 6 3/4 miles
oh, and I almost forgot the probability of Knightmare walking
6 3/4 miles is inversely proportional to the quantity of beer remaining in the fridge ... or something like that ... need verification from Cam and Chris!
:)
jeez! I forgot ... 6 3/4 miles is one way ... for a total of 13 1/2 miles. I'm not even sure the inversely proportional "thingy" could justify that distance.
mmmmmmm .... did I actually say "thingy" ... wow, been listening to my daughter too closely :)
LOL
btw..my refrigerator running out of beer is a nightmare in it's self
i don't like this one Zaux,it scares me too much
Ok...on the way there, he walks 1 1/2 miles per hour.
On the way back, he walks 4 1/2 miles per hour.
So the trip to will take 3 times as long as the trip back.
Basically, you divide 6 by 4, getting 1.5, then multiply by 3 to get the amount of time spent walking to the store and 1 1/2 miles per hour.
so it took him 4 and a half hours of walking 1.5 miles per hour to get to the store.
4.5 x 1.5 = 6.75 miles to the store.
To check the answer, do the same thing for walking back home.
1.5 hours x 4.5 miles per hour = 6.75 miles.
-Soli
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