To find out how long it will take Iris to complete the entire floor, we first need to determine her rate of work.
Iris sweeps 23 of the floor in \( \frac{1}{3} \) of an hour.
The first step is to find out how much of the floor she can sweep in 1 hour. Since \( \frac{1}{3} \) of an hour is one-third of an hour, we can calculate her rate as follows:
\[ \text{Rate} = \frac{23 \text{ (part of the floor)}}{\frac{1}{3} \text{ hour}} = 23 \times 3 = 69 \text{ (parts of the floor per hour)} \]
Next, we know that the entire floor is considered as 1 (or 100% of the floor). To find out how long it will take her to sweep the entire floor, we can divide the full job (1 part of the floor) by her rate:
\[ \text{Time to complete entire floor} = \frac{1 \text{ (whole floor)}}{69 \text{ (parts per hour)}} = \frac{1}{69} \text{ hours} \]
Now, since she can complete 69 parts in an hour, we can summarize that she would take approximately:
\[ \frac{1}{69} \text{ of an hour} \approx 0.01449 \text{ hours} \approx 0.868 \text{ minutes} \]
Since this might be confusing, let’s clarify: She completes the entire sweeper measurement over about 0.01449 hours, which is just a little over half a minute. Since no answer choices seem to represent this, let's try again with how many times larger \( \frac{1}{3} \) of an hour is when represented in classical numeric form – without approximating speed but finding out how much time it equates clearly.
Calculating it this way, she needs to multiply the effort by three to scale to the hour for only once completing all 23 situations, leading too lethargically slower than proposed rates, pointing towards \( \frac{69}{23} = 3 \) hours.
Thus, the correct response ensuring we're diligent in coverage will fall closest:
- 23 hours
So the time it takes her to complete the entire gym floor at the given speed is 23 hours.
1 answer