A stenographer has been asked to fill out 500 forms. She fills 25 forms in half an hour. Another stenographer joins her, who fills 45 forms per hour. How long will the entire assignment take?

This is a work-rate problem requiring us to calculate individual and combined work rates. The key is to account for the initial work done by the first stenographer alone before the second one joins.

• First stenographer's rate: 25 forms / 0.5 hour = 50 forms/hour.
• In the first half-hour, the first stenographer completes 25 forms.
• Remaining forms to fill: 500 total forms - 25 forms = 475 forms.
• The second stenographer's rate is 45 forms/hour.
• When they work together, their combined rate is 50 forms/hour + 45 forms/hour = 95 forms/hour.
• Time taken to fill the remaining 475 forms together: 475 forms / 95 forms/hour = 5 hours.
• Total time for the entire assignment: 0.5 hours (initial) + 5 hours (together) = 5.5 hours.

Option A (5 hours) would be correct if they started working together from the beginning. Options C and D are incorrect calculations, failing to correctly combine the work rates or account for the initial work period.