Question 148680: Three questions that I am certain have quite simple solutions but for some reason they escape me. Thank you in advance for you help!
In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
I know how to find the probability of drawing one of any given color -- 3/11, 4/11, and 4/11 but that's as far as I can get.
A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
My guess was that you would take the average of 10 and 8, the answer being 9. The answer key stated 8.9. I have no idea how to get that answer.
Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
Clueless on this one. Does it have something to do with weighted averages?
-Paloma
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
4 blue followe by 4 green followed by 1 red would be the maximum number of
draws to get at least one of each color:
Ans: 9
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A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
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Time out = d/r = x/10 hrs
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Time in = d/r = x/8 hrs
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Round-trip DATA:
distance = 2x ; time = [(x/10) + (x/8)] = (18x/80) = (9x/40) hrs
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So average rate for the round trip = d/r = (2x)/(9x/40)= 80x/9x =
= 80/9 = 8.8888888... mph ; rounding down you get 8.9 mph
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Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
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Johnathan rate = (20/40) = (1/2) page/min
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Susan rate = (20/30) = (2/3) page/min
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Together DATA:
rate + rate = together rate
(1/2) + (2/3) = 1/x page/min
(7/6) = 1/x page min
x = (6/7) min for one page
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20(6/7) = 120/7 = 17.14 minutes for 20 pages
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Cheers,
Stan H.
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