291. 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?
- A. 6 hours
- B. 5 hours
- C. 5 1/2 hours
- D. 4 1/2 hours
Check answer and explanation
Answer: 5 1/2 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.