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?

প্রশ্নে বলা হচ্ছে, Bill এবং Ben একত্রে 6 ঘণ্টায় একটি গ্যারেজ পরিষ্কার করে। Bill একা পরিষ্কার করতে 10 ঘণ্টা সময় নিলে Ben কত সময় নিবে?

(Bill + Ben) একত্রে 6 ঘণ্টায় করে 1 টি কাজ

∴ (Bill + Ben) একত্রে। ঘণ্টায় করে $=\frac{1}{6}$ টি কাজ

আবার, Bill একা 10 ঘণ্টায় করে 1 টি কাজ

∴ Bill একা 1 ঘণ্টায় করে $=\frac{1}{10}$ টি কাজ

∴ Ben একা 1 ঘণ্টায় করে $=\frac{1}{6}-\frac{1}{10}=\frac{5-3}{30}=\frac{2}{30}=\frac{1}{15}$ অংশ।

অর্থাৎ Ben একা 15 ঘণ্টায় কাজটি করবে।

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.