## anonymous one year ago help please i will reward you

1. anonymous

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own.

2. Kash_TheSmartGuy

what's the question?

3. anonymous

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own.

4. anonymous

@jim_thompson5910

5. jim_thompson5910

x = time it takes Jimmy to do the job alone x-8 = time it takes Harry to do the job alone (since he can do it 8 hrs faster) you can form this equation based off of the given word problem $\Large \frac{1}{x} + \frac{1}{x-8} = \frac{1}{3}$ solve for x to get your answer

6. anonymous

okay so now i just have to find the common denominator and combine?

7. anonymous

would it take him 26 hours to do it on hs own @jim_thompson5910

8. anonymous

@mns

9. jim_thompson5910

$\Large \frac{1}{x} + \frac{1}{x-8} = \frac{1}{3}$ $\Large 3x(x-8)*\left(\frac{1}{x} + \frac{1}{x-8}\right) = 3x(x-8)*\left(\frac{1}{3}\right)$ $\Large 3x(x-8)*\left(\frac{1}{x}\right) + 3x(x-8)*\left(\frac{1}{x-8}\right) = 3x(x-8)*\left(\frac{1}{3}\right)$ $\Large 3(x-8) + 3x = x(x-8)$ I'll let you take over

10. jim_thompson5910

In step 2, I multiply both sides of the equation by the LCD 3x(x-8) to clear out all the fractions (which are fully cleared out by step 4)

11. jim_thompson5910

oh sorry line 3 is cut off, it is supposed to be $3x(x-8)*\left(\frac{1}{x}\right) + 3x(x-8)*\left(\frac{1}{x-8}\right) = 3x(x-8)*\left(\frac{1}{3}\right)$