# need help w/ 'Ray can pick all of the oranges in 1 row...'

#### mathdunce23

##### New member
Ray can pick all of the oranges in 1 row of a grove in 6 hours. Asa can pick all of the oranges in 1 row of the grove in 4 hours. if they work together, how long will it take them to pick 15 rows of the grove?
this problem has stumped me. I really need help on this one! Please help me to understand how to get the right answer. thanks a trillion. :mrgreen:

#### soroban

##### Elite Member

Hello, mathdunce23!

Ray can pick all of the oranges in 1 row of a grove in 6 hours.
Asa can pick all of the oranges in 1 row of the grove in 4 hours.
If they work together, how long will it take them to pick 15 rows of the grove?

Try this baby-talk approach on these "Work" problems.

$$\displaystyle \text{Ray can pick one row in 6 hours.}$$
. . $$\displaystyle \text{In one hour, he can pick }\frac{1}{6}\text{ of a row.}$$

$$\displaystyle \text{Asa can pick one row in 4 hours.}$$
. . $$\displaystyle \text{In one hour, he can pick }\frac{1}{4}\text{ of a row.}$$
$$\displaystyle \text{Together, in one hour, they can pick: }\:\frac{1}{6} + \frac{1}{4} \:=\:\frac{5}{12}\text{ of a row.}$$
$$\displaystyle \text{In }x\text{ hours, they can pick }\frac{5}{12}x\text{ rows.}$$

$$\displaystyle \text{If they pick 15 rows, we have: }\;\frac{5}{12}x \:=\:15\quad\Rightarrow\quad x \:=\:36$$

$$\displaystyle \text{Therefore, working together, it will take them }\boxed{36\text{ hours}}\text{ to pick 15 rows.}$$