Word Problems

[ammomyers]

Ok, here are two that I am sure are just unsolveable:

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone?

AND

Jeff takes 5 hrs longer to build a fence that it takes Bill. When they work together, it takes them 6 hours. How long would it take Bill to do the job alone?

 

[soroban]

Hello, ammomyers!

You can baby-talk your way through these . . .

An experienced accountant can balance the books twice as fast as a new accountant.
Working together it takes the accountants 10 hours.
How long would it take the experienced accountant working alone?

\(\displaystyle \text{The experienced accountant takes }x\text{ hours.}\)
. . \(\displaystyle \text{In one hour, he can do }\tfrac{1}{x}\text{ of the job.}\)

\(\displaystyle \text{The new accountant takes }2x\text{ hours.}\)
. . \(\displaystyle \text{In one hour, he can do }\tfrac{1}{2x}\text{ of the job.}\)

\(\displaystyle \text{Together, in one hour, they can do: }\:\frac{1}{x} + \frac{1}{2x}\text{ of the job.}\)


\(\displaystyle \text{But working together, they take 10 hours to do the job.}\)
. . \(\displaystyle \text{That is, in one hour, they can do }\tfrac{1}{10}\text{ of the job.}\)


\(\displaystyle \text{There is our equation! }\;\hdots\quad \frac{1}{x} + \frac{1}{2x} \:=\:\frac{1}{10}\)

Got it?


Use the same approach on the second problem.

 

[ammomyers]

Ok, I get it with the x's, when you don't know how how long it would take, but once you throw the numbers in the mix I am so confused. This is my biggest problem with Math! I just can't talk my way through the problems!

Oh, and by the way, thank you so much! I am jealous you can so this so fast! I have been working on these two problems for HOURS

 

[Denis]

Jeff takes 5 hrs longer to build a fence that it takes Bill. When they work together, it takes them 6 hours.
How long would it take Bill to do the job alone?

A good idea is for YOU to make up a simple case, so you can "see" what goes on;
like, there's a candy bowl containining 100 candies;
Art can eat only 5 per hour: so it takes Art 100/5 = 20 hours to eat the full bowl;
Ben can eat 20 per hour: so it takes Ben 100/20 = 5 hours to eat the full bowl;
TOGETHER they eat 5+20 = 25 per hour: 100/25 = 4 hours to eat the full bowl.

So using that example, the question would be:
Art takes 15 hrs longer to eat a bowl of candies than it takes Ben. When they work together, it takes them 4 hours. How long would it take Ben to do the job alone?

Get my drift?

 

[Deleted member 4993]

Jeff takes 5 hrs longer to build a fence that it takes Bill. When they work together, it takes them 6 hours.
How long would it take Bill to do the job alone?

A good idea is for YOU to make up a simple case, so you can "see" what goes on;
like, there's a candy bowl containining 100 candies;
Art can eat only 5 per hour: so it takes Art 100/5 = 20 hours to eat the full bowl;
Ben can eat 20 per hour: so it takes Ben 100/20 = 5 hours to eat the full bowl;
TOGETHER they eat 5+20 = 25 per hour: 100/25 = 4 hours to eat the full bowl.

Now Ben and Art can get tummy-ache together!!!

So using that example, the question would be:
Art takes 15 hrs longer to eat a bowl of candies than it takes Ben. When they work together, it takes them 4 hours. How long would it take Ben to do the job alone?

Get my drift?