Question

Abi can do a piece of work in 8 days, ali in 10 days and aaron in 15 days. they all start the work together, but abi leaves the work after 2 days and aaron leaves 5/3 days before the work is completed. how many days did the work last?

Answer 1

here is your answer...

Answer 2

The work lasted for 5 days.

GIVEN

Number of days Abi can complete a work = 8 days

Number of days Ali can complete a work = 10 days

Number of days Aaron can complete a work = 15 days

TO FIND

Number of days the work last.

SOLUTION

We can simply solve the above problem as follows;

Days taken by Abi to complete 1 work = 8 days

Abi's work in 1 day = 1/8

Days taken by Ali to complete 1 work = 10 days

Ali's work in 1 day = 1/10

Days taken by Aaron to complete 1 work = 15 days

Aaron's 1 day work = 1/15

Combined work done by Abi, Ali and Aaron in 1 day = 1/8 + 1/10 + 1/15

= 15 + 12 + 8

= 35/120

= 7/24

Let the work lasted for x days

Abi's 2 day work + Aaron's (x - 5/3) days work + Ali's x days work = 1

$2 \times \frac{1}{8} + x \times \frac{1}{10} + x - \frac{5}{3} \times \frac{1}{15} = 1$

$\frac{1}{4} + \frac{x}{10} + \frac{x - 1.6}{15} = 1$

LCM of 4, 10, 15 = 60

$\frac{15 + 6x + 4x - 6.4 }{60} = 1$

$8.6 + 10x = 60$

10x = 51.4

x = 51.4/10 = 5.14

5.14 ≈ 5 days

Hence, The work lasted for 5 days.

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