1.Jeff can weed the garden in 4 h. His wife takes the same amount of time. After they worked for 1 hr, their son helped them finish in 1/2 h. H long would it have taken Rory by himself to weed the garden?

Question

1.Jeff can weed the garden in 4 h. His wife takes the same amount of time. After they worked for 1 hr, their son helped them finish in 1/2 h. H long would it have taken Rory by himself to weed the garden?

Answer 1

eh?

mom and pop each do 1/4 job in 1 hour
so, 1/2 job remained when Rory came to work.

In the next 1/2 hour, mom and pop each did another 1/8 of the job, or 1/4 combined.

That left 1/4 of the job for Rory to do in 1/2 hour. So, Rory could do the whole job in 2 hours by himself.

Answer 2

To find out how long it would have taken Rory to weed the garden by himself, we can break down the given information step by step.

First, we need to determine how much work Jeff and his wife can do in 1 hour together. Since Jeff can weed the garden in 4 hours, he can complete 1/4 of the work in 1 hour. Since his wife takes the same amount of time, she can also complete 1/4 of the work in 1 hour. Therefore, together, Jeff and his wife can complete 1/4 + 1/4 = 1/2 of the work in 1 hour.

Next, we know that after working for 1 hour, Jeff and his wife were helped by their son, who finished the remaining work in 1/2 hour. This tells us that in total, Jeff, his wife, and their son completed 1/2 of the work in 1/2 hour. Therefore, they completed 1/2 of the work in 1/2 hour.

Finally, we need to find out how much work is left to be done for Rory to complete the entire garden on his own. We know that together, Jeff, his wife, and their son completed 1/2 of the work in 1/2 hour, which means they have completed half of the total work. Therefore, the other half of the work is still remaining for Rory to complete.

Let's denote the time it would take Rory to complete the remaining half of the work as 'x' hours.

Since Rory would be working alone, he would have to complete 1/2 of the work in 'x' hours. Therefore, we can set up the equation:
1/2 = 1/x

To solve for 'x', we can cross multiply:
1x = 2 * 1/2
x = 2

Hence, it would have taken Rory 2 hours to complete the remaining half of the work on his own.

Answer 3

jeff's rate = 1/4

wife's rate = 1/4
combined rate = 1/4 + 1/4 = 1/2

job done after 1 hr = (1/2)(1 hr) = 1/2

let son's rate be 1/x , (who is Rory ? )

combined rate = 1/4 + 1/4 + 1/x
= 1/2 + 1/x
= (x+1)/(2x)

time for rest of job = (1/2)/combined rate)
(1/2)/((x+1)/(2x))
= (1/2)(2x/(x+1)
= x/(x+1)

but x/(x+1) = 1/2 hr
2x = x+1
x = 1

So Rory could do the garden in 1 hour by himself