Respuesta :
Answer:
Sohan
Step-by-step explanation:
she was the one who made it faster to do the work!!
The reciprocal of the time it takes to do the work together is the sum of
the reciprocal of the time it takes to do the work individually.
- Sohan will take the least number of days (40 days) to do the work
Reasons
Let R represent the number of days it will take Rohan, S, the number of
days it would take Sohan, and M, the number of days it would take Mohan
to do the work alone, we have;
[tex]\displaystyle \frac{1}{30} = \mathbf{ \frac{1}{R} + \frac{1}{S}}[/tex]...(1)
[tex]\displaystyle \frac{1}{24} = \mathbf{ \frac{1}{M} + \frac{1}{S}}[/tex]...(2)
[tex]\displaystyle \mathbf{ \frac{1}{40}} = \frac{1}{R} + \frac{1}{M}[/tex]...(3)
Subtract equation (1) from equation (2) and add the result to equation (3), we have;
[tex]\displaystyle \frac{1}{24} - \frac{1}{30} =\displaystyle \left( \frac{1}{M} + \frac{1}{S} \right) - \left(\frac{1}{R} + \frac{1}{S}\right) =\displaystyle \left( \frac{1}{M} - \frac{1}{R} \right)[/tex]
[tex]\displaystyle \frac{1}{24} - \frac{1}{30} + \frac{1}{40} =\displaystyle \left( \frac{1}{M} - \frac{1}{R} \right) + \frac{1}{R} + \frac{1}{M} = \frac{2}{M}[/tex]
[tex]\displaystyle \mathbf{\frac{1}{24} - \frac{1}{30} + \frac{1}{40}} = \frac{1}{30} = \frac{2}{M}[/tex]
M = 2 × 30 = 60
- M = 60
[tex]\displaystyle \frac{1}{24} = \mathbf{\frac{1}{M} + \frac{1}{S}}[/tex]
[tex]\displaystyle \frac{1}{24} = \frac{1}{60} + \frac{1}{S}[/tex]
[tex]\displaystyle \frac{1}{24} - \frac{1}{60} =\frac{1}{40} = \frac{1}{S}[/tex]
[tex]\displaystyle \frac{1}{S} = \frac{1}{40}[/tex]
- S = 40
[tex]\displaystyle \frac{1}{40} = \frac{1}{R} + \frac{1}{M}[/tex]
[tex]\displaystyle \frac{1}{40} = \mathbf{\frac{1}{R} + \frac{1}{60}}[/tex]
[tex]\displaystyle \frac{1}{40} - \frac{1}{60} = \frac{1}{120} = \frac{1}{R}[/tex]
- R = 120
Therefore;
- The one who takes the least number of days to do the work is Sohan, S = 40
Learn more about work rate word problem here:
https://brainly.com/question/14696505
