If it takes Steve 6 hours to tile a floor and Cheryl 4 hours to tile the same floor, how long would it take both Steve and Cheryl to tile the floor if they worked together?
- 2 hours 12 minutes
- 2 hours 24 minutes
- 3 hours
- 3 hours 12 minutes
- 10 hours
Answer(s): B
Explanation:
Let x = the part of the floor that can be tiled in 1 hour. Since Steve can tile a floor in 6 hours, he can tile 1/6 of the floor in 1 hour. Since Cheryl can tile the same floor in 4 hours, she can tile 1/4 of the floor in 1 hour. Use the equation 1/6 + 1/4 = 1/x, where 1/x represents the part of the floor they can tile in an hour together. Multiply each term by the LCD = 12x. 12x × 1/6 + 12x × 1/4 = 12x × 1/x. The equation simplifies to 2x + 3x = 12.5x =
12. Divide each side by 5 to get x = 12/5 =2.4 hours. Since 0.4 times 60 minutes equals 24 minutes, the final answer is 2 hours 24 minutes.
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