X can do a piece of work in 8 days, Y can do it in 10 days and Z can do it in 20 days. In how many days can X, Y and Z together complete the work?
Question
X can do a piece of work in 8 days, Y can do it in 10 days and Z can do it in 20 days. In how many days can X, Y and Z together complete the work?
Solution
Sure, here's how you can solve this problem:
Step 1: Find out how much work each person can do in a day. This is done by taking the reciprocal of the number of days it takes for each person to complete the work.
- X can do 1/8 of the work in a day.
- Y can do 1/10 of the work in a day.
- Z can do 1/20 of the work in a day.
Step 2: Add up the amount of work each person can do in a day to find out how much work they can do together in a day.
- Together, X, Y, and Z can do (1/8 + 1/10 + 1/20) of the work in a day.
Step 3: Simplify the fraction.
- The least common multiple of 8, 10, and 20 is 40. So, convert each fraction to have 40 as the denominator.
- X can do 5/40 of the work in a day.
- Y can do 4/40 of the work in a day.
- Z can do 2/40 of the work in a day.
- Together, X, Y, and Z can do (5/40 + 4/40 + 2/40) = 11/40 of the work in a day.
Step 4: To find out how many days they can complete the work together, take the reciprocal of the fraction from step 3.
- X, Y, and Z together can complete the work in 40/11 days, which is approximately 3.64 days.
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