Question

Two women renu and usha are working on an embroidery design. if usha worked alone, she would need eight hours more to complete the design than if they both worked together. now if renu worked alone, it would need 4.5 hours more to complete the design than they both working together. what time would it take renu alone to complete the design?

Answer 1

Answer:

Time would it take Renu alone to complete the design is 10.5 hrs.

Step-by-step explanation:

Given : Two women renu and usha are working on an embroidery design. if usha worked alone, she would need eight hours more to complete the design than if they both worked together.

Now if renu worked alone, it would need 4.5 hours more to complete the design than they both working together.

To find : What time would it take renu alone to complete the design?

Solution :

Let the both will complete work in x hours.

Their combine efficiency = $\frac{1}{x}$

Usha's work = x + 8

and her efficiency = $\frac{1}{x+8}$

like this way Renu's work = x + 4.5

and her efficiency = $\frac{1}{x+4.5}$

Now, Total efficiency is

$\frac{1}{x+8}+\frac{1}{x+4.5}=\frac{1}{x}$

$\frac{1}{x+4.5}=\frac{1}{x}-\frac{1}{x+8}$

$\frac{1}{x+4.5}=\frac{x+8-x}{x(x+8)}$

$\frac{1}{x+4.5}=\frac{8}{x(x+8)}$

$x(x+8) = 8(x+4.5)$

$x^2=40$

$x=\sqrt{40}$

$x=6.3$

Approximately x=6

Time would it take Renu alone to complete the design is

=6 + 4.5

=10.5 hr.