Question

A and B working together can finish a job in 3
hours, while A can finish the job alone in 5 hours.
What fraction of the job does A do, when A and B
work together?​

Answer 1

Answer

Given,

• A and B can finish a job in 3hr
• A can finish the job alone in 5hr

To find,

• Fraction of the job does A do when A and B work together

Solution ,

Let A finish his job in x hr

Let B finish his job in y hr

One hr job of A :

⇛ $\implies \sf \frac { 1 } { x }$

One hr job of B :

⇛ $\implies \sf \frac { 1 } { y}$

According to the question :

⇛ $\sf \frac { 1 } { x } + \frac { 1 } { y} = \frac { 1 } { 3 }$

x = 5 ( given )

⇛ $\sf \frac { 1 } { 5} + \frac { 1 } { y} = \frac { 1 } { 3 }$

⇛ $\sf \frac { 1 } { y } = \frac { 1 } { 3 } - \frac { 1 } { 5 }$

⇛ $\sf \frac { 1 } { y } = \frac { 5 - 3} { 15}$

⇛ $\sf \frac { 1 } { y } = \frac { 2} { 15}$

⇛ $\sf y = \frac { 15 } { 2 }$

⇛ Hence B can do the work in $\sf \frac { 15 } { 2 }$ hr

So,

One hr work of B = $\sf \frac { 2 } { 15 }$

Given that both A & B work together for 3hr

Hence in 3 hr B will do :

⇛ $\sf 3 × \frac { 2 } { 15 }$ fraction of work

i.e $\sf \frac { 2 } { 5 }$

Hence A will do $\sf 1 - \frac { 2 } { 5 }$ fraction of work

⇛ $\rm \frac { 5 - 2 } { 5 }$

i.e $\sf \frac { 3 } { 5 }$ fraction of work

Hence we got that:

• Fraction of work A does : $\sf \frac { 3 } { 5 }$

• Fraction of work B does : $\sf \frac { 2 } { 5 }$