Question

14 Tom can whitewash a fence alone in 4 hours, and Huck can whitewash the same fence in 5 hours working by himself. Tom whitewashes with Huck for 1 hour and then leaves. How long will it take Huck to finish whitewashing the fence?

Answer 1

To determine how long it will take Huck to finish whitewashing the fence after Tom leaves, calculate the work done together in the first hour, subtract from the total, and then divide the remaining work by Huck's work rate.

Step-by-step explanation:

Firstly, to solve this problem, we need to establish the rate at which both Tom and Huck can independently complete whitewashing the fence. Tom can whitewash a fence in 4 hours, which means his work rate is 1/4 of the fence per hour. Huck, on the other hand, can whitewash the same fence in 5 hours, so his work rate is 1/5 of the fence per hour.

Since they worked together for 1 hour, we add their rates together to find the amount of work done in that hour. So, we have 1/4 + 1/5 = 5/20 + 4/20 = 9/20 of the fence has been whitewashed in the first hour.

Subsequently, 11/20 of the fence remains to be whitewashed by Huck alone. Since Huck whitewashes at a rate of 1/5 per hour, we can determine how many hours it will take him to complete the remaining work by dividing the remaining work, 11/20, by his rate, 1/5. This results in (11/20) / (1/5) which simplifies to 11/20 * 5/1 = 55/20 = 2.75 hours. Therefore, Huck will take an additional 2.75 hours to finish whitewashing the fence after Tom leaves.

Answer 2

Given:

Time it takes Tom = 4 hours

Time it takes Huck = 5 hours

Tom then whitewashes with Huck for 1 hour and then leaves.

Let's find how long it will take Huck to finish whitewashing the fence.

We have:

Tom's rate = 1/4

Huck's rate = 1/5

Total rate:

`(1)/(4)+(1)/(5)=x`

Now, let's find the time it will take them to whitewash together.

`\begin{gathered} (1)/(T)=(5+4)/(20) \\ \\ (1)/(T)=(9)/(20) \\ \\ T=(20)/(9) \\ \\ T=2.22 \end{gathered}`

It will take them 2.22 hours to whitewash together.

Now they both whitewash together for 1 hour before Huck leaves.

We have:

`2.22-1=1.22`

When Huck leaves after one hour, the time left for both of them to finish together is 1.22 hours.

Since only Huck will finish whitewashing the fence, the time it will take him will be:

`5(1-(1.22)/(2.22))=2.25`

Therefore, it will take Huck to finish whitewashing the fence is 2.25 hours.

ANSWER:

2.25 hours