A stenographer has been asked to fill out 500 forms. she fills 25 forms by the end of half an hour when she is joined by another stenographer who fill the forms at the rate of 45 per hour. The entire assignment will be carried out in?
- 4 1/2 hours
- 5 hours
- 5 1/2 hours
- 6 hours
Explanation
Let's break down the problem to determine if the total time taken is indeed 5 1/2 hours.
Step 1: Determine how many forms are left after the first half-hour
In the first half-hour, the stenographer fills 25 forms.
Total forms remaining: 500−25=475 forms
Step 2: Determine the combined rate of both stenographers
The first stenographer's rate: 25 / 0.5 =50 forms per hour
The second stenographer's rate: is 45 forms per hour
Combined rate: 50+45=95 forms per hour
Step 3: Calculate the time needed to complete the remaining forms
Time needed: 475 / 95 ≈5 hours
Step 4: Calculate the total time for the entire assignment
Time for the first 25 forms: 0.5 hours
Time for the remaining forms: 5 hours
Total time: 0.5+5=5.5 hours
So, the entire assignment will indeed take 5 1/2 hours to complete.
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