What are the explicit and recursive formulas for the sequence 540, 180, 60, 20, ...?
1 answer:
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Answer:
Jim's hose: 27 hours.
Bob's hose: 21.6 hours.
Step-by-step explanation:
Let t represent hours taken by Jim's hose.
Part of pool filled by Jim's hose in 1 hour would be .
We have been given that Bob's hose, used alone, takes 20% less time than Jim's hose alone. This means that Bob's hose take will take 80% time of Jim's hose that is .
Part of pool filled by Bob's hose in 1 hour would be .
We are also told that it takes 12 hours using both hoses. Part of pool filled by both hoses in 1 hour would be .
Now, we will add rates of both hoses and equate with as:
Cross multiply:
Therefore, it will take 27 hours for Jim's hose to fill the pool alone.
Time take by Jim's hose alone: .
Therefore, it will take 21.6 hours for Bob's hose to fill the pool alone.