Answer:
[tex] \boxed{37.5 \: \: \: minutes}[/tex]
Step-by-step explanation:
Let's solve:
[tex] \mathsf {people \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: time( \: in \: minutes) }[/tex]
[tex] \mathsf{5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 hour = 60 minutes}[/tex]
[tex] \mathsf{8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x}[/tex]
Here, Let 8 people take x minutes to complete the work.
Since, the number of people and their working minutes are indirect proportional. So,
Here, the ratio of people = 5 : 8
The ratio of minutes = 60 : x
So,
[tex] \mathsf{ \frac{5}{8} = \frac{x}{60} }[/tex]
Apply cross product property
⇒[tex] \mathsf{8x = 60 \times 5}[/tex]
Multiply the numbers
⇒[tex] \mathsf{8x = 300}[/tex]
Divide both sides of the equation by 8
⇒[tex] \mathsf {\frac{8x}{8} = \frac{300}{8} }[/tex]
Calculate
⇒[tex] \mathsf{x = 37.5 \: minutes}[/tex]
Hope I helped!
Best regards!
