Bill and Ben can clean the garage. together in 6 hours. If it takes Bill 10 hours working alone, how long will it take Ben working alone?
Let's use the concept of work rates to solve this problem.
Let B represent Bill's work rate (how much of the garage he can clean in one hour), and let C represent Ben's work rate.
According to the problem, Bill and Ben can clean the garage together in 6 hours, so their combined work rate is 1/6 of the garage per hour.
So, we can write the equation: B + C = 1/6
Now, it's given that Bill takes 10 hours to clean the garage alone, so his work rate is 1/10 of the garage per hour: B = 1/10
We want to find out how long it takes Ben to work alone, which means we need to find C.
Now, we can substitute B into the first equation: (1/10) + C = 1/6
To isolate C, we'll subtract 1/10 from both sides of the equation: C = 1/6 - 1/10
To subtract these fractions, we need a common denominator, which is 30: C = (5/30) - (3/30)
C = 2/30
Now, simplify the fraction: C = 1/15
So, Ben's work rate is 1/15 of the garage per hour, which means it would take him 15 hours to clean the garage alone. Therefore, the answer is 15 hours.
ঐকিক নিয়ম (Unitary Methods):
একটি জিনিসের দাম, ওজন, পরিমাণ ইত্যাদি বের করে নির্দিষ্ট সংখ্যক এই জাতীয় জিনিসের দাম, ওজন, পরিমাণ ইত্যাদি বের করার নিয়মকে ঐকিক নিয়ম বলে।
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