A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours,the number of hours taken by the father,to do the job alone is?Options1342
Question
A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours,the number of hours taken by the father,to do the job alone is?Options1342
Solution
To solve this problem, we first need to understand that the rate of work done is inversely proportional to the time taken to complete the work.
Step 1: Calculate the rate of work for each son. The first son completes the job in 3 hours, so his work rate is 1/3 of the job per hour. The second son completes the job in 6 hours, so his work rate is 1/6 of the job per hour.
Step 2: Add the sons' rates together. The combined work rate of the two sons is (1/3 + 1/6) = 1/2 of the job per hour.
Step 3: Since the father can do the job as fast as his two sons working together, his work rate is also 1/2 of the job per hour.
Step 4: To find out how long it takes the father to do the job alone, we take the reciprocal of his work rate. So, the father takes 1 / (1/2) = 2 hours to do the job alone.
So, the correct answer is 2 hours.
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