Algebra work word problem. help please? :(

Question

 Mei can pick forty bushels of apples in six hours. One day her friend Cody helped her and it only took 3.75 hours. Find how long it would take Cody to do it alone.

Answer 1

The fact that they are picking 40 bushels of apples is extra information. All that really matters is the time it took.

 

Every hour, Mei completes 1/6 of the job.  Together, they complete 1/3.75 of the job.  Since we don't know Cody's time, we'll say he took x hours and that his rate is 1/x of the job every hour.

 

If you add Mei's rate and Cody's rate, you'll get the combined rate.

 

1/6 + 1/x = 1/3.75

 

If we find a common denominator, we can add the fractions on the one side.  The common denominator is 6x.

 

x/6x + 6/6x = 1/3.75

(x+6)/6x = 1/3.75

 

This is now a proportion and we can solve by cross-multiplying.

 

6x · 1 = 3.75 · (x + 6)

6x = 3.75x + 22.5

2.25x = 22.5

x = 10

 

It would take Cody 10 hours to complete the job alone.