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A mother is 3 times faster than her daughter. If the daughter completes a piece of work in 15 days, how long will it take for both mother and daughter to complete the same work?
- a)13/4 days
- b)15/4 days
- c)17/4 days
- d)19/4 days
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A mother is 3 times faster than her daughter. If the daughter complet...
Daughter’s one-day work = 1/15
Mother’s one-day work = 1/5
Both can complete their work = 1/5+1/15 = (3+1)/15 = 4/15
Hence, required days= 15/4 days .
Most Upvoted Answer
A mother is 3 times faster than her daughter. If the daughter complet...
Understanding the Problem
To solve the problem, we need to determine how long it will take for both the mother and daughter to complete a piece of work together, given that the mother is 3 times faster than her daughter.
Work Rate of the Daughter
- The daughter completes the work in 15 days.
- Therefore, her work rate is:
- 1/15 of the work per day.
Work Rate of the Mother
- Since the mother is 3 times faster than her daughter:
- Her work rate becomes:
- 3 * (1/15) = 3/15 = 1/5 of the work per day.
Combined Work Rate
- To find the combined work rate of both the mother and daughter:
- Combined rate = Work rate of mother + Work rate of daughter
- Combined rate = (1/5) + (1/15)
Finding a Common Denominator
- The common denominator for 5 and 15 is 15:
- Convert (1/5) to (3/15).
- Now, add the two rates:
- Combined rate = (3/15) + (1/15) = 4/15 of the work per day.
Time Taken to Complete the Work Together
- To find the total time taken to complete the work when both work together:
- Time = 1 / Combined rate
- Time = 1 / (4/15) = 15/4 days.
Conclusion
Thus, when both the mother and daughter work together, they can complete the work in 15/4 days, which corresponds to option 'B'.
To solve the problem, we need to determine how long it will take for both the mother and daughter to complete a piece of work together, given that the mother is 3 times faster than her daughter.
Work Rate of the Daughter
- The daughter completes the work in 15 days.
- Therefore, her work rate is:
- 1/15 of the work per day.
Work Rate of the Mother
- Since the mother is 3 times faster than her daughter:
- Her work rate becomes:
- 3 * (1/15) = 3/15 = 1/5 of the work per day.
Combined Work Rate
- To find the combined work rate of both the mother and daughter:
- Combined rate = Work rate of mother + Work rate of daughter
- Combined rate = (1/5) + (1/15)
Finding a Common Denominator
- The common denominator for 5 and 15 is 15:
- Convert (1/5) to (3/15).
- Now, add the two rates:
- Combined rate = (3/15) + (1/15) = 4/15 of the work per day.
Time Taken to Complete the Work Together
- To find the total time taken to complete the work when both work together:
- Time = 1 / Combined rate
- Time = 1 / (4/15) = 15/4 days.
Conclusion
Thus, when both the mother and daughter work together, they can complete the work in 15/4 days, which corresponds to option 'B'.
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A mother is 3 times faster than her daughter. If the daughter completes a piece of work in 15 days, how long will it take for both mother and daughter to complete the same work?a)13/4 daysb)15/4 daysc)17/4 daysd)19/4 daysCorrect answer is option 'B'. Can you explain this answer?
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