16) Time and Work Aptitude

1) Worker A completes a task in 8 days and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?

A. 40 days.

B. 40 days. 이

C. 40 days. 8

D. 40 days

Give me the right option

To solve this problem, we'll calculate how long it takes for both workers A and B to complete the task together.

**Step 1: Calculate the rate at which each worker completes the task.**

- Worker A completes the task in 8 days, so A's work rate is \( \frac{1}{8} \) of the task per day.
- Worker B completes the task in 10 days, so B's work rate is \( \frac{1}{10} \) of the task per day.

**Step 2: Calculate their combined work rate.**

When A and B work together, their combined work rate is the sum of their individual work rates:

\[
\text{Combined rate} = \frac{1}{8} + \frac{1}{10}
\]

To add these fractions, find a common denominator:

\[
\frac{1}{8} + \frac{1}{10} = \frac{5}{40} + \frac{4}{40} = \frac{9}{40}
\]

So, the combined work rate is \( \frac{9}{40} \) of the task per day.

**Step 3: Calculate the time it takes for both to complete the task together.**

If they can complete \( \frac{9}{40} \) of the task in one day, then the time \( T \) required to complete the whole task is:

\[
T = \frac{1}{\frac{9}{40}} = \frac{40}{9} \text{ days} \approx 4.44 \text{ days}
\]

Since this does not match any of the given options, it appears there is a formatting error in the options. The correct time should be approximately **4.44 days**, but among the options listed:

**None of the options is correct.**

Let me know if you need more clarification or details.

Here are 5 related questions for practice:

1. Worker C can finish a task in 12 days, and Worker D in 15 days. How long will it take them to complete the task together?
2. If Worker E completes a task in 6 days and Worker F in 9 days, how many days will it take if they work together?
3. Worker G can finish a task in 5 days, and Worker H in 7 days. What is the combined time they need to complete the task?
4. How many days will it take two workers to complete a task together if one takes 4 days and the other takes 6 days?
5. Worker I and Worker J can complete a task together in 3 days. If Worker I works alone, it takes 9 days. How long does Worker J take?

**Tip:** Always check the units and ensure you interpret the question correctly, especially when multiple workers or resources are involved in solving a problem.

Learn how to solve a time and work aptitude problem involving Worker A completing a task in 8 days and Worker B in 10 days. Discover the combined work rate concept and calculate the time taken for both workers to complete the task together. Suitable for students in Grades 7-9.

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