ground
Clear frame
Inverse Proportion (2)
Q5 people take 12 mins to change all of the light bulbs in a
restaurant. How long would it take 3 people to change all of
the light bulbs?



Answer :

Sure, let's work through this problem step by step.

We have a situation where 5 people take 12 minutes to change all the light bulbs in a restaurant. We need to find out how long it would take for 3 people to do the same task.

1. Identify the relationship: This is a classic example of an inverse proportion. When more people are working together, they usually take less time to complete a task. Conversely, when fewer people are working, it takes more time.

2. Constant product method: In inverse proportion, the product of the number of people and the amount of time taken remains constant. Let's call this product the "constant."

- For 5 people taking 12 minutes, the constant would be:
[tex]\[ \text{constant} = \text{number of people} \times \text{time taken} = 5 \times 12 \][/tex]
So,
[tex]\[ \text{constant} = 60 \][/tex]

3. Set up the equation for the new situation: Now, we need to find the time it would take 3 people to complete the task. Let's call this time [tex]\( T \)[/tex].

- Using the constant from above, we set up the equation:
[tex]\[ \text{constant} = \text{number of people} \times \text{time taken} = 3 \times T \][/tex]
- Plugging in the value of the constant:
[tex]\[ 60 = 3 \times T \][/tex]

4. Solve for [tex]\( T \)[/tex]:
[tex]\[ T = \frac{60}{3} \][/tex]
[tex]\[ T = 20 \][/tex]

So, it would take 3 people 20 minutes to change all of the light bulbs in the restaurant.