If x can finish a job in 4 hours and y can finish the same job in 8 hours independently, then they together will finish the job in:

Options

A. 160 minutes
B. 150 minutes
C. 140 minutes
D. 120 minutes

Answer

To solve the problem of how long X and Y will take to finish the job together, we can follow these steps:

### Step 1: Determine the work rates of X and Y
- X can finish the job in 4 hours. Therefore, the work rate of X is:
\[ \text{Work rate of X} = \frac{1 \text{ job}}{4 \text{ hours}} = \frac{1}{4} \text{ jobs per hour} \]

- Y can finish the job in 8 hours. Therefore, the work rate of Y is:
\[ \text{Work rate of Y} = \frac{1 \text{ job}}{8 \text{ hours}} = \frac{1}{8} \text{ jobs per hour} \]

### Step 2: Combine the work rates
- To find the combined work rate of X and Y when they work together, we add their individual work rates:
\[ \text{Combined work rate} = \text{Work rate of X} + \text{Work rate of Y} = \frac{1}{4} + \frac{1}{8} \]

### Step 3: Find a common denominator
- The common denominator for 4 and 8 is 8. We can rewrite the work rates:
\[ \frac{1}{4} = \frac{2}{8} \]
- Now, we can add the work rates:
\[ \text{Combined work rate} = \frac{2}{8} + \frac{1}{8} = \frac{3}{8} \text{ jobs per hour} \]

### Step 4: Calculate the time taken to complete the job together
- If their combined work rate is \(\frac{3}{8}\) jobs per hour, we can find the time taken to complete 1 job by taking the reciprocal of the combined work rate:
\[ \text{Time taken} = \frac{1 \text{ job}}{\frac{3}{8} \text{ jobs per hour}} = \frac{8}{3} \text{ hours} \]

### Step 5: Convert hours into minutes
- To convert \(\frac{8}{3}\) hours into minutes, we multiply by 60 minutes/hour:
\[ \frac{8}{3} \text{ hours} \times 60 \text{ minutes/hour} = 160 \text{ minutes} \]

### Final Answer
- Therefore, X and Y together will finish the job in **160 minutes**.

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