Respuesta :
Answer:
168 minutes
Step-by-step explanation:
It takes 120 minutes for the first person to clean the jellyfish tank.
This means that in 1 minute the first person cleans [tex]\[\frac{1}{120}\] [/tex] of the tank.
Let the time taken by the second person working alone to clean the tank be x minutes.
Then in 1 minute the second person cleans [tex]\[\frac{1}{x}\] [/tex] of the tank.
Working together, the two persons clean,
[tex]\[\frac{1}{120} + \frac{1}{x}\] [/tex] of the tank
But it is given that the two persons working together can clean the tank in 70 minutes. This means that in 1 minute both of them can clean [tex]\[\frac{1}{70}\] [/tex] of the tank.
Expressing in equation form:
[tex]\[\frac{1}{120} + \frac{1}{x} = \frac{1}{70}\] [/tex]
[tex]\[=> \frac{1}{x} = \frac{1}{70} - \frac{1}{120} \] [/tex]
[tex]\[=> \frac{1}{x} = \frac{12-7}{840} \] [/tex]
[tex]\[=> \frac{1}{x} = \frac{5}{840} \] [/tex]
[tex]\[=> \frac{1}{x} = \frac{1}{168} \] [/tex]
[tex]\[=> x = 168 \] [/tex]
This means that the second person can clean the tank in 168 minutes.
