Question

30 students can do work in 120mins. How long would 90 students take to do the same work at the same rate?

Answer 1

[AI-generated answer — Bot GPT 3.5]

We can set up a proportion to solve this problem. Let's let x represent the number of minutes it would take for 90 students to do the same work.

We can set up the proportion:

30 students can do work in 120 mins
90 students can do work in x mins

Using a proportion, we can solve for x:

30/120 = 90/x

Cross-multiplying gives us:

30x = 120*90

Dividing both sides by 30:

x = (120*90)/30

x = 360

Therefore, it would take 90 students 360 minutes to do the same work at the same rate.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find out how long it would take 90 students to do the same work at the same rate, we can use the formula:

work = rate * time

Given:

30 students can do the work in 120 minutes.

Let's assume that the rate at which each student works is constant. Thus, the rate of each student is 1/120 of the work per minute.

To find out how long it would take 90 students to do the same work, we can rearrange the formula:

work = rate * time

time = work / rate

The work remains the same because it is the same work being done.

work = 1

rate of 1 student = 1/120

rate of 90 students = 90 * (1/120) = 3/4

time = 1 / (3/4)

time = 4/3

Therefore, it would take 90 students approximately 1 hour and 20 minutes (4/3 hours) to do the same work at the same rate.

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we need to use the concept of "work rate."

Given:
- 30 students can do the work in 120 minutes.
- We want to find out how long it would take 90 students to do the same work at the same rate.

Step 1: Find the work rate for 30 students.
Since 30 students can complete the work in 120 minutes, the work rate of 30 students can be calculated as:
Work rate = (Work done) / (Time taken) = 1 / 120.

Step 2: Calculate the work rate for 90 students.
If we assume that the work rate is proportional to the number of students, then the work rate for 90 students can be calculated by multiplying the work rate for 30 students by the ratio of the number of students:
Work rate for 90 students = Work rate for 30 students * (90/30).

Step 3: Find the time taken for 90 students to complete the work.
To find the time taken for 90 students to complete the same work, we divide the work done by the work rate for 90 students:
Time taken = (Work done) / (Work rate for 90 students).

Step 4: Calculate the final answer.
Substitute the value of the work rate for 30 students and the work rate for 90 students into the time formula and solve for the time taken for 90 students.

Time taken = (Work done) / (Work rate for 90 students)
Time taken = (1) / [(1 / 120) * (90 / 30)]
Time taken = 1 / [(1 / 120) * 3]
Time taken = 1 / (1/40)
Time taken = 40 minutes.

Therefore, it would take 90 students to complete the same work in 40 minutes at the same rate as 30 students did in 120 minutes.