Question

If Rodger can completely paint a room on his own in 6 hours,

and both Sara and Rodger together can completely paint a
room in 4 hours, is Sara working at a pace to allow her to
paint the room on her own in 7 hours or less?

Answer 1

Sara cannot paint the room on her own in 7 hours or less.

Step-by-step explanation:

To determine if Sara can paint the room on her own in 7 hours or less, we first need to find her painting rate. Let's assume Sara's painting rate is x rooms per hour. Since Sara and Rodger together can completely paint a room in 4 hours, their combined painting rate is 1 room per 4 hours.

Using the formula (Sara's rate + Rodger's rate) = Combined rate, we can write the equation (x + 1/6) = 1/4. Solving for x, we find that Sara's painting rate is 1/12 rooms per hour.

To determine if Sara can paint the room on her own in 7 hours or less, we can calculate the time it takes for her to paint the room alone using her painting rate. Multiplying her rate (1/12) by the number of hours (7), we find that she can paint approximately 0.583 rooms in 7 hours. Since she cannot paint a complete room in 7 hours, the answer is no.

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