A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

Appeared in: NORCET 1 - 2020

Explanation

The fundamental principle of 'Time and Work' problems is that the rate of work is the reciprocal of the time taken.
A's rate of work is 1/6 of the job per day, and B's rate is 1/9 of the job per day.
When working together, their rates are additive: (1/6) + (1/9) = (3+2)/18 = 5/18 of the job per day.
The total time taken is the reciprocal of the combined rate: 1 / (5/18) = 18/5, which equals 3.6 days.

Option A: This is the arithmetic average of the two times ((6+9)/2 = 7.5). This method is incorrect for combining work rates, as working together must result in a shorter time than the fastest individual.
Option C: This value (5.4) is the result of an incorrect calculation (e.g., multiplying 6 by 0.9). It does not follow the correct formula for combined work.
Option D: This would be the correct answer only if both individuals took 6 days to complete the work. In that case, their combined rate would be 1/6 + 1/6 = 2/6 = 1/3 of the work per day, taking 3 days total.

Visual 1: Flowchart: Step-by-step process for solving combined work problems. Step 1: Find individual rates (1/A, 1/B). Step 2: Add the rates (1/A + 1/B). Step 3: Find the reciprocal of the sum to get the total time.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating combined work rate and time as background academic context rather than a clinical decision trigger.
This type of question tests basic numeracy and logical reasoning, skills essential for various calculations in a clinical setting, such as medication dosage, IV drip rates, and interpreting data over time.
What if? If B could work twice as fast (in 4.5 days), the combined time would be (6 × 4.5) / (6 + 4.5) = 27 / 10.5 ≈ 2.57 days. This demonstrates how a more efficient partner significantly reduces the total time.

How to Approach the Question

Identify the task: Calculate the combined time for two people working together.
Step 1: Determine the individual rate of work for each person. The rate is the reciprocal of the time taken (e.g., if time is 'x' days, the rate is 1/x of the work per day).
Step 2: Calculate A's rate (1/6) and B's rate (1/9).
Step 3: Add the individual rates to find the combined rate of work per day: (1/6) + (1/9).
Step 4: Find the reciprocal of the combined rate. This gives the total number of days required to complete the work together.
Alternatively, use the shortcut formula for two people: Time = (Time A × Time B) / (Time A + Time B).

Concept Tested & Keywords

Q_iuo1C_FRr6Ku7BSdsStD

Practise the full NORCET 1 - 2020

Attempt every question from this paper in a timed mock, then review the full solution for each one.