Question

Gab does one-seventh of a job in 3 hours. If Torres works 1.5 hours more than Gab, he can finish one-tenth of the job. How long does it take to do the job if they work together?

Answer 1

It would take 14.3 hours to complete the work together.

Step-by-step explanation:

Let us assume  if they work together, the work is completed in t hours.

So, the work completed by both workers in 1 hour  = $(\frac{1}{t} )$

The amount of time taken by Gab to finish 1/ 7 of job  = 3 hours

So, the amount of time taken to finish the job  = 3 x 7 = 21 hours

So, the fraction of job completed by gab in 1 hour  = $(\frac{1}{21} )$  ... (1)

The amount of time taken by Torres to finish 1/ 10 of job  = (3 + 1.5)  hours

So, the amount of time taken to finish the job  = 4.5 x 10 = 45 hours

So, the fraction of job completed by Torres in 1 hour  = $(\frac{1}{45} )$

So, the amount of work completed by Gab and Torres in 1 hour  = $(\frac{1}{21} ) + (\frac{1}{45} )$

$\implies \frac{1}{21} + \frac{1}{45} = \frac{1}{t} \\\implies \frac{45+ 21}{21 \times 45} = \frac{1}{t}\\\implies \frac{66}{945} = \frac{1}{t}\\\implies t = \frac{945}{66}= 14.3$

Hence, it would take 14.3 hours to complete the work together.