Question 894099: 1. kim read 2 1/4 times as many pages on saturday as on sunday. she reads 120 pages more on a saturday. how many pages did she read altogether?
2. a tank can be filled by pipe a in five hours and by pipe b in 8 hours with each working on its own.when the tank is full and drainage hole is open the water is drained in 20 hours. if initially the tank was empty and it started the two pumps together but left the drainage open, how long does it take for the tank to be filled:?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
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problem number 1:
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kim reads 2.25 times as many pages on saturday as on sunday.
she reads 120 more pages on saturday then on sunday.
let x = the number of pages she reads on sunday.
the formula for saturday is y = 2.25 * x because she reads 2.25 times the number of pages that she reads on sunday.
y is the number of pages she reads on saturday.
x is the number of pages she reads on sunday.
the formula for this saturday is y = 120 + x because she reads 120 pages on this saturday than she does on this sunday.
presumably the reading os 2.25 times the pages on sunday holds true for all saturdays and sundays, including this saturday and sunday.
the problem is not worded very well and is therefore confusing but i think i understand what they mean.
you have 2 equations for what she reads on this saturday.
they are:
y = 2.25 * x
and:
y = 120 + x
y is what she reads on saturday.
x is what she reads on sunday.
since she reads the same number of pages on this saturday using both formulas, then the formulas must be equivalent and you get:
2.25 * x = 120 + x
subtract x from both sides of the equation to get 2.25 * x - x = 120
simplify this to get 1.25 * x = 120
divide both sides of this equation by 1.25 to get x = 120 / 1.25.
simplify to get x = 96
she reads 96 pages on this sunday.
she reads 2.25 * 96 = 216 pages on this saturday.
she reads 96 + 120 = 216 pages on this saturday.
both formulas get you to the same number which is what i believe is what the problem wants you to find.
you are basically solving two equations simultaneously and you get a solution that is common to both equations.
that solution is x = 96.
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problem number 2:
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pipe A fills the tank in 5 hours.
the rate at which pipe A fills the tank is therefore 1/5 of the tank every hour.
similarly, the rate that pipe B fills the tank is 1/8 of the tank every hour.
similarly, the rate that the drain empties the tank is 1/20 of the tank every hour.
in 5 hours, working at the rate of 1/5 of the tank per hour, pipe A has filled the tank.
you get 5 * 1/5 = 1 which represents one full tank.
similarly, pipe B has filled the tank in 8 hours because 1/8 * 8 = 1 and 1 represents 1 full tank.
similarly, the drain empties the tank in 20 hours because 1/20 * 20 = 1 and 1 represents 1 drained tank.
when they work together, the rates are additive.
when they work against each other, the rates are subtractive.
the formula for the 2 pipes working with each other against the drain is:
(r1 + r2 - r3) * T = 1
r1 is the rate of fill of pipe A.
r2 is the rate of fill of pipe B.
r3 is the rate of the drain.
you get:
(1/5 + 1/8 - 1/20) * T = 1
put all the fractions under a common denominator and you get:
(8/40 + 5/40 - 2/40) * T = 1
add them together and you get 11/40 * T = 1
divide both sides of this equation by 11/40 and you get T = 40/11 hours.
in 40/11 hours, pipe A has filled 40/11 * 8/40 = 320/440 of the tank.
in 40/11 hours, pipe B has filled 40/11 * 5/40 = 200/440 of the tank.
in 40/11 hours, the drain has drained 40/11 * 2/40 = 80/440 of of the tank.
add the first two up together and subtract the third to get 440/440 of the tank which is equal to one full tank.
in 40/11 hours you have one full tank with both pipes filling against an open drain.
that's equivalent to 3.636363.... hours.
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