Question

ruby can assemble 2 22 gift baskets by herself in 7 77 minutes. emma can assemble 4 44 gift baskets by herself in 15 1515 minutes. ruby begins assembling gift baskets at 1 : 00 p.m. 1:00p.m.1, colon, 00, start text, p, point, m, point, end text, and emma begins assembling gift baskets at 1 : 15 p.m. 1:15p.m.1, colon, 15, start text, p, point, m, point, end text if they continue to work at the above rates, at what time will they finish the 5 4 th 54 th 54, start superscript, start text, t, h, end text, end superscript basket?

Answer 1

To find out the time when Ruby and Emma will finish the 54th basket, we need to determine their rates and calculate the time needed.

Step-by-step explanation:

To find out when Ruby and Emma will finish the 54th basket, we need to determine how many baskets they can each assemble in one minute. Ruby can assemble 2/22 baskets in 7/77 minutes, which simplifies to 1/11 baskets in 1/77 minutes. Emma can assemble 4/44 baskets in 15/1515 minutes, which simplifies to 2/1515 baskets in 1/1515 minutes.

Next, we need to find their combined rate. Ruby's rate is 1/11 baskets per 1/77 minutes, and Emma's rate is 2/1515 baskets per 1/1515 minutes. To add their rates, we need a common denominator. The least common multiple of 77 and 1515 is 116385, so we need to convert both rates to have a denominator of 116385.

After calculating the combined rate, we can determine the time needed to assemble the 54th basket by dividing the number of baskets by the combined rate. We can then add this time to the starting time of 1:00 p.m. to find the finishing time.

Answer 2

Ruby will finish assembling the 54th basket at 2:22 p.m., and Emma will finish at 9:00 a.m.

Step-by-step explanation:

Ruby can assemble 2 gift baskets in 77 minutes, while Emma can assemble 4 gift baskets in 1515 minutes. To determine when they will finish the 54th basket, we need to calculate the total time each of them takes to assemble a single basket and then multiply it by 54.

For Ruby: 77 minutes / 2 baskets = <<77/2=38.5>>38.5 minutes per basket

For Emma: 1515 minutes / 4 baskets = <<1515/4=378.75>>378.75 minutes per basket

Now we can calculate the total time it would take for each of them to finish the 54th basket:

For Ruby: 38.5 minutes/basket * 54 baskets = 2082 minutes

For Emma: 378.75 minutes/basket * 54 baskets = 20445 minutes

Since they start at different times, Ruby at 1:00 p.m. and Emma at 1:15 p.m., we need to add the times they start to the total time it takes for each of them:

• For Ruby: 1 hour (60 minutes) + 2,082 minutes = 2142 minutes
• For Emma: 1 hour and 15 minutes (75 minutes) + 20,445 minutes = 20,520 minutes

After converting the minutes to hours, Ruby will finish the 54th basket at 2:22 p.m. and Emma will finish at 9:00 a.m.