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Ahmad needs 6 days to finish a project alone whereas Abu needs 9 days to finish ...

Apr 16, 2024

Ahmad needs 6 days to finish a project alone whereas Abu needs 9 days to finish the project alone. They first work together for 2 days, then the project is left for Abu to finish on his own. how many days does Abu need to finish the remaining project?

Generated Graph

Solution by Steps

step 1

Calculate the rate at which Ahmad and Abu work together

step 2

Ahmad's rate is

\frac{1}{6}

of the project per day, and Abu's rate is

\frac{1}{9}

of the project per day. Together, they complete

\frac{1}{6} + \frac{1}{9}

of the project per day

step 3

To find their combined rate, calculate

\frac{1}{6} + \frac{1}{9} = \frac{3}{18} + \frac{2}{18} = \frac{5}{18}

of the project per day

step 4

In 2 days, they complete

2 \times \frac{5}{18} = \frac{10}{18} = \frac{5}{9}

of the project

step 5

The remaining part of the project is

1 - \frac{5}{9} = \frac{4}{9}

of the project

step 6

Abu needs to complete the remaining

\frac{4}{9}

of the project on his own

step 7

Since Abu completes

\frac{1}{9}

of the project per day, he will need

\frac{4}{9} \div \frac{1}{9} = 4

days to finish the remaining project

Answer

Abu needs 4 more days to finish the remaining project.

Key Concept

Work Rate and Combining Individual Rates

Explanation

To solve this problem, we calculate the combined work rate of Ahmad and Abu, determine how much of the project they complete together, and then find out how long it takes Abu to finish the remaining part of the project alone.