Ruby can assemble 2 gift baskets by herself in 7 minutes. Emma can assemble 4 gift baskets by herself in 15 minutes. Ruby begins assembling gift baskets at 1:00 p.m., and Emma begins assembling gift baskets at 1:15 p.m. If they continue to work at the above rates, at what time will they finish the 54^("th ") basket? Choose 1 answer: (A) 2:30 p.m. (B) 2:42p.m. (c) 2:45 p.m. (D) 3:00p.m.

Question

Ruby can assemble 2 gift baskets by herself in 7 minutes. Emma can assemble 4 gift baskets by herself in 15 minutes. Ruby begins assembling gift baskets at 1:00 p.m., and Emma begins assembling gift baskets at 1:15 p.m. If they continue to work at the above rates, at what time will they finish the  54^("th ") basket? Choose 1 answer: (A) 2:30 p.m. (B)  2:42p.m. (c)  2:45 p.m. (D)  3:00p.m.

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Determine Rate for Ruby: Determine the rate at which Ruby can assemble gift baskets. Ruby can assemble 2 baskets in 7 minutes, so her rate is 2 baskets per 7 minutes.Determine Rate for Emma: Determine the rate at which Emma can assemble gift baskets. Emma can assemble 4 baskets in 15 minutes, so her rate is 4 baskets per 15 minutes.Convert Rates to Baskets per Minute: Convert the rates to baskets per minute. Ruby's rate is $ \frac{2}{7} $ baskets per minute. Emma's rate is $ \frac{4}{15} $ baskets per minute.Calculate Combined Rate: Calculate the combined rate when both Ruby and Emma are working together. The combined rate is $ \frac{2}{7} + \frac{4}{15} $ baskets per minute.Find Least Common Denominator: Find the least common denominator (LCD) to add the rates. The LCD of 7 and 15 is 105.Express Rates with LCD: Express both rates with the LCD as the denominator. Ruby's rate is $ \frac{30}{105} $ baskets per minute. Emma's rate is $ \frac{28}{105} $ baskets per minute.Add Rates for Combined Rate: Add the rates to get the combined rate. The combined rate is $ \frac{30}{105} + \frac{28}{105} = \frac{58}{105} $ baskets per minute.Calculate Time for 54 Baskets: Calculate the number of minutes it will take to assemble 54 baskets at the combined rate. We need to divide the total number of baskets by the combined rate: $ \frac{54}{\frac{58}{105}} $.Ruby Works Alone Before Emma: Perform the division to find the number of minutes. $ \frac{54}{\frac{58}{105}} = 54 \times \frac{105}{58} \approx 98.28 $ minutes.Calculate Time for Remaining Baskets: Ruby starts at 1:00 p.m. and works alone for 15 minutes before Emma starts. In 15 minutes, Ruby assembles $ \frac{2}{7} \times 15 = \frac{30}{7} \approx 4.29 $ baskets.Add Time for Ruby and Emma: Subtract the number of baskets Ruby assembles alone from the total number of baskets. 54 - 4.29 = 49.71 baskets remaining to be assembled together.Convert Total Minutes to Hours: Calculate the number of minutes it will take to assemble the remaining baskets at the combined rate. $ \frac{49.71}{\frac{58}{105}} = 49.71 \times \frac{105}{58} \approx 89.98 $ minutes.Add Time to Start Time: Add the time Ruby worked alone to the time both will work together. 15 minutes (Ruby alone) + 89.98 minutes (together) = 104.98 minutes.Convert the total minutes to hours and minutes. 104.98 minutes is 1 hour and 44.98 minutes.Add this time to the start time of 1:00 p.m. 1:00 p.m. + 1 hour and 44.98 minutes is approximately 2:45 p.m.

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