If Jimmy takes 6 hours and Bobby takes 3 hours to rake the yard separately, how long will it take them working together?

To determine how long it will take Jimmy and Bobby to rake the yard together, we start by calculating their individual work rates.

Jimmy rakes the yard in 6 hours, which means his work rate is 1/6 of the yard per hour. Similarly, Bobby rakes the yard in 3 hours, giving him a work rate of 1/3 of the yard per hour.

When they work together, we can add their rates of work:

• Jimmy's rate: 1/6 yards per hour

• Bobby's rate: 1/3 yards per hour

To add these rates, we find a common denominator, which is 6. We convert Bobby's rate:

1/3 = 2/6

Now we can add the rates:

1/6 + 2/6 = 3/6 = 1/2

This combined rate means together they can rake 1/2 of the yard in one hour. To find out how long it takes them to complete the entire yard, we take the reciprocal of their combined rate:

1 / (1/2) = 2 hours.

Thus, it will take Jimmy and Bobby 2 hours to rake the yard when