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) 2:42 p.m. (C) 2:45 p.m. (D) 3:00 p.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) 2:42 p.m. (C) 2:45 p.m. (D) 3:00 p.m.

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Determine Ruby's Rate: Determine Ruby's rate of assembling gift baskets. Ruby can assemble 2 baskets in 7 minutes, so her rate is: Rate = Number of baskets / Time Rate = 2 baskets / 7 minutesDetermine Emma's Rate: Determine Emma's rate of assembling gift baskets. Emma can assemble 4 baskets in 15 minutes, so her rate is: Rate = Number of baskets / Time Rate = 4 baskets / 15 minutesCalculate Ruby's Baskets: Calculate the number of baskets Ruby can assemble from 1:00 p.m. to 1:15 p.m. Since Ruby starts at 1:00 p.m. and Emma starts at 1:15 p.m., Ruby will have a 15-minute head start. Ruby's rate is 2 baskets / 7 minutes, so in 15 minutes she can assemble: Number of baskets = Rate * Time Number of baskets = (2/7) baskets/minute * 15 minutes Number of baskets = 30/7 Number of baskets = 4.2857... Ruby can assemble 4 baskets in her first 15 minutes (since she cannot assemble a fraction of a basket, we only count the whole baskets).Calculate Combined Rate: Calculate the combined rate of Ruby and Emma. Ruby's rate is 2 baskets / 7 minutes, and Emma's rate is 4 baskets / 15 minutes. To combine their rates, we add them together: Combined rate = Ruby's rate + Emma's rate Combined rate = (2/7) + (4/15) To add these fractions, we need a common denominator, which is 105. Combined rate = (30/105) + (28/105) Combined rate = (58/105) baskets/minuteCalculate Remaining Baskets: Calculate the number of baskets remaining after Ruby's head start. Ruby has already assembled 4 baskets, so there are 54 - 4 = 50 baskets left to assemble.Calculate Time Remaining: Calculate the time it will take for Ruby and Emma to assemble the remaining 50 baskets. Time = Number of baskets / Combined rate Time = 50 baskets / (58/105) baskets/minute Time = 50 * (105/58) minutes Time = 5000/58 minutes Time = 86.2069... minutesConvert Time to Hours: Convert the time to hours and minutes. 86.2069 minutes is 1 hour and 26.2069 minutes. Since we only need whole minutes, we round down to 26 minutes.Add Time to Finish: Add the time to Emma's start time to find the finish time. Emma started at 1:15 p.m., so adding 1 hour and 26 minutes gives us: Finish time = 1:15 p.m. + 1 hour and 26 minutes Finish time = 2:41 p.m. However, we rounded down the minutes, so the actual finish time will be a minute or two later.Choose Closest Time: Choose the closest time option that is after 2:41 p.m. The closest time option after 2:41 p.m. is (B) 2:42 p.m.

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