SOLUTION: The irrigation system needs about 3 times as long to complete a job as another irrigation system. When both systems operate at the same time the job can be completed in 9 hrs. How

Question 40407: The irrigation system needs about 3 times as long to complete a job as another irrigation system. When both systems operate at the same time the job can be completed in 9 hrs. How long does it take the fast system to do the job alone?
____hrs
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Malik purchased a pair of roller blades that were originally priced at $250 for a sale price of $180. He charged the roller blades on his credit card and made the minimum monthly payment of $20. When he received his first statement, he read that the minimum finance charge for each month that there was a balance on the card that would be $15. If Malik waited until he had the $250 cash in his hand to pay for the roller blades, how much money would he save?
Thanks
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let t = the time for the faster system to do the job
faster rate + slower rate = combined rate
(1 job / t) + (1 job / 3t) = 1 job / 9 hours
1/t + 1/3t = 1/9
3t is the LCD
3/3t + 1/3t = 1/9
(3 + 1) / 3t = 1/9
3t = 4*9
t = 36/3
t = 12 hours answer
check:
1/t + 1/3t = 1/9
1/12 + 1/(3*12) = 1/9
1/12 + 1/36 = 1/9
3/36 + 1/36 = 1/9
4/36 = 1/9
1/9 = 1/9
OK
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Out of the min monthly payment of $20 comes the $15 for each month
there is a balence, so he has $5 per month to put towards the $180
purchase
$180 / $5/month = 36 months
With the last payment, there is no balence due, so there's no
finance charge. That means there's only 35 months of $15 finance charges
($15 / month)*(35 months) = $525
$525 + $180 = $705 total paid out
$705 - $250 = $455 savings if he just paid $250 for roller blades
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