A man can complete a work in 10 days, while another can do it in 15 days. If the

A man can complete a work in 10 days, while another can do it in 15 days. If they work together, how long will it take to complete the work?

A man can complete a work in 10 days, while another can do it in 15 days. If they work together, how long will it take to complete the work?

Step 1: Understand that the first man can complete the work in 10 days. This means he does 1/10 of the work in one day.
Step 2: Understand that the second man can complete the work in 15 days. This means he does 1/15 of the work in one day.
Step 3: To find out how much work they can do together in one day, add their daily work rates: 1/10 + 1/15.
Step 4: To add 1/10 and 1/15, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert 1/10 to 3/30 (because 1 * 3 = 3 and 10 * 3 = 30) and 1/15 to 2/30 (because 1 * 2 = 2 and 15 * 2 = 30).
Step 6: Now add the two fractions: 3/30 + 2/30 = 5/30.
Step 7: Simplify 5/30 to 1/6 (because both 5 and 30 can be divided by 5).
Step 8: This means together they complete 1/6 of the work in one day.
Step 9: To find out how many days it takes to complete the whole work, take the reciprocal of 1/6, which is 6.
Step 10: Therefore, if they work together, they will complete the work in 6 days.

Work Rate – Understanding how to calculate the work rate of individuals and combine their rates to find the total work done.
Fraction Addition – Adding fractions with different denominators to find a common work rate.
Time Calculation – Calculating the total time taken to complete a task based on combined work rates.