Please explain this math problem!?

Question

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

A. 2.4 hr
B. 24 hr
C. 36 hr
D. 15 hr

Please show your work.

Answer 1

In one hour, Ray will pick 1/6 of a row. Asa will pick 1/4 of a row.

If they are working together, they will pick 1/6 + 1/4 of the row every hour.

1/6 + 1/4 = 2/12 + 3/12 = 5/12

If they pick 5/12 of the row in an hour, it takes 12/5 hours to pick a row.

12/5 hr/rw * 15 rw = 180/5 hr = 36 hr

Answer 2

This may not be the simplest solution, but it works. I used the old D = RxT formula, where distance = rate x time. In this case, "distance" refers to the number of rows picked. Since the times for the two boys must be the same, I changed the formula to read T = D/R, so we just equate the two D/R's.

Let D = no. of rows Ray pics, so (15-D) = no. of rows Asa picks. Ray's rate is 1/6 of a row per hour. Asa's rate is 1/4 of a row per hour. Therefore for Ray, D/R = D/1/6, or 6D. For Asa, D/R would be (15-D)/1/4, or 4(15-D).

So if the times are equal, 6D = 4(15-D). Simplify, and you get 6D = 60 - 4D. Add 4D to both sides, 10D = 60, and D = 6. Go back to the statements, and Ray picked 6 rows, and Asa picked (15-6) = 9 rows. Ray took 6x6 hours = 36 hours, and Asa took 9x4 hours = 36 hours.

There's probably a simpler way to do it.

Answer 3

The best way to figure this one out is to determine their hourly rates of orange picking. Ray does a row every 6 hours, so that means that he can pick exactly 1/6 of a row every hour.
Asa can pick a whole row in 4 hours, which mean that she can pick exactly 1/4 row per hour.

Together, how much can they pick per hour?
1/6 + 1/4 = 4/24 + 6/24 = 10/24 = 5/12 per hour.

So, how many hours would it take them to pick 15 rows? 15, divided by 5/12 = 36 hours.

Answer 4

ray can pick 1/6 rows in an hour

asa can pick 1/4 rows in an hour

together,

1/6 + 1/4 = 2/12 + 3/12 = 5/12 rows in an hour

5/12 rows ------- 1 hr
15 rows -------- ? hr (direct proportion)

36 hr

Answer 5

You handle workload questions like this by finding out how much work is done in 1 unit of time rather than how many units of time are required to do 1 unit of work.

Ray can pick 1 row in 6 hours, hence in 1 hour he can pick 1/6 row.

Asa can pick 1 row in 4 hours, so in 1 hour he can pick 1/4 row.

Now if they work together, in 1 hour they can pick 1/6 + 1/4 rows = 2/12 + 3/12 = 5/12 row.

so 5/12 row is picked in 1 hour by the two of them
so 1 row is picked in 12/5 hours by the two together.
hence 15 rows is picked in 12/5 * 15 hours