word problem

[franklin91]

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 50% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?

I am completely lost and honestly dont know where to start....can someone please help me

 

[mmm4444bot]

This exercise is a "work-type" problem; you can google for examples.

We look at the fractional part of the task completed per unit of time.

In this exercise, the time unit is hours.

If it takes 18 hours to complete the task, then 1/18th of the task is completed per hour.

Let x = the hours Jim's hose requires to complete the task alone

Then x/2 = the hours Bob's hose requires to complete the task alone

This means that Jim's hose completes 1/xth of the job each hour and that Bob's hose completes 2/xth of the job each hour.

Working together, these two fractional amounts must add up to 1/18th of the job each hour.

1/x + 2/x = 1/18

Clarified that my initial pronoun refers to the type of exercise, not to the OPs subject line.

 

[franklin91]

thank you so so much....i am sorry for the mistake of the work and word problem....i was really confused....work problems are really a struggle for me...thank you for the help

 

[soroban]

Hello, franklin91!

Here's another approach for talking your way through the problem.

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.
They know that it takes 18 hours using both hoses.
They also know that Bob's hose, used alone, takes 50% less time than Jim's hose alone.
How much time is required to fill the pool by each hose alone?

\(\displaystyle \text{Let }\,B\text{ = number of hours for Bob's hose to fill the pool.}\)

\(\displaystyle \text{In one hour, it fills }\frac{!}{B}\text{ of the pool.}\)

\(\displaystyle \text{In 18 hours, it fills }\frac{18}{B}\text{ of the pool.}\) .[1]


\(\displaystyle \text{Bob's hose takes half as long as Jim's hose.}\)

\(\displaystyle \text{That is, Jim's hose takes }twice\text{ as long as Bob's hose.}\)

. . \(\displaystyle 2B\text{ = number of hours for Jim's hose to fill the pool.}\)

\(\displaystyle \text{In one hour, it fills }\frac{1}{2b}\text{ of the pool.}\)

\(\displaystyle \text{In 18 hurs, it fills }\frac{18}{2B}\text{ of the pool.}\) .[2]


\(\displaystyle \text{So, in 18 hours, the two hoses fill }\frac{18}{B} + \frac{18}{2B}\text{ of the pool.}\)

\(\displaystyle \text{But we know that, in 18 hours, they fill the entire pool (one pool).}\)

\(\displaystyle \text{There is our equation! }\quad\hdots\quad \boxed{\frac{!8}{B} + \frac{18}{2B} \:=\:1}\)


\(\displaystyle \text{Multiply by }2B\!:\;\;36 + 18 \:=\:2B \quad\Rightarrow\quad B \:=\:27\)

. . \(\displaystyle \text{Then: }\;J \:=\;2B \:=\:54\)


\(\displaystyle \text{Therefore: }\;\begin{Bmatrix}\text{Bob's hose alone takes 27 hours.} \\ \text{Jim's hose alone takes 54 hours.} \end{Bmatrix}\)