Solve the 4 parts of the following question A Krystal can wa

Solve the 4 parts of the following question:

A. Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only took 5.76 minutes. How long would it take Perry to do it alone?

B. Working alone, Dan can sweep a porch in 15 minutes. Alberto can sweep the same porch in 11 minutes. If they worked together how long would it take them?

C. Ryan can paint a fence in ten hours. Asanji can paint the same fence in eight hours. If they worked together how long would it take them?

D. Working alone, it takes Asanji eight hours to dig a 10 ft by 10 ft hole. Brenda can dig the same hole in nine hours. How long would it take them if they worked together?

Please show all work and give full explanations. No handwritten work please.

Solution

A. Let us assume that Perry, alone, can wax the floor in x minutes. Then she can wax 1/x of the floor in 1 minute. Krystal can wax the floor in 16 minutes. Then Krysrtal can wax 1/16 of the floor in 1 minute. Then Krystal and perry together can wax ( 1/16 + 1/x ) = ( x + 16) /16x of the floor in 1 minute. Then both of them together can wax the entire floor in 16x / (x + 16) minutes. Therefore, we have 16x / (x + 16) = 5.76 or, 16x = 5.76 (16 + x) or, 16x = 92.16 + 5.76x or, 16x - 5.76x = 92.16 or, 10.24x = 92.16. Therefore, x = 92.16/10.24 = 9 minutes. Thus Perry alone can wax the floor in 9 minutes.

B. Dan can sweep the floor in 15 minutes. Therefore, he can sweep 1/15 of the floor in 1minute. Alberto can sweep the floor in 11 minutes.Therefore, he can sweep 1/11 of the floor in 1minute. Thus, Dan and Alberto together, can sweep 1/15 + 1/11 = 26/ 165 of the floor in 1 minute. Then, they, together can sweep the entire floor in 165/26 = 6.3462 minutes, i.e. in 6 minutes, 21 seconds approximately.

C. Ryan can paint a fence oin 10 hours. Therefore, he can paint 1/10 th of the fence in 1 hour. Asanji can paint the same fence in 8 hours.

D. Asanji can dig a 10ft by 10ft hole in 8 hours. Therefore, Asanji can dig 1/8 th of the hole in 1 hour. Brenda can dig the same hole in 9 hours. Therefore, Brendai can dig 1/9 th of the hole in 1 hour. Then, Asanji and Breda together can dig 1/8 + 1/9 = 17/72 of the hole in 1 hour. Thus, Therefore, Asanji and Breda together can dig the entire hole in 72/17 = 4.23529 hours or, 4 hours, 14 minutes 7 seconds approximately. Therefore, Asanji can paint 1/8 th of the fence in 1 hour. Then Ryan and Asanji, working together, can paint !/10 + 1/8 = 9/40 of the fence in 1 hour. Thus, Ryan and Asanji, working together, can paint the entire fence in 40/9 hours or, 4.4444 hours or, 4 hors, 26 minutes, 40 seconds approximately.