1 Solve the 4 parts of the Following Question A Working alon

1. Solve the 4 parts of the Following Question:

A. Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same hole in six hours. How long would it take them if they worked together?

B. Shawna can pour a large concrete driveway in six hours. Dan can pour the same driveway in seven hours. Find how long it would take them if they worked together.

C. It takes Trevon ten hours to clean an attic. Cody can clean the same attic in seven hours. Find how long it would take them if they worked together.

D. Working alone, Carlos can oil the lanes in a bowling alley in five hours. Jenny can oil the same lanes in nine hours. If they worked together how long would it take them?

Please show all work and give full explanations. Please no handwritten work. Thanks.

Solution

Add their rates of digging to get
the rate of them digging together
Ryan\'s rate:
(1 hole/5 hrs)
Castel\'s rate:
(1 hole /6 hrs)
I want to add their rates for 1hole

No. of hours working together—x:

x/5 +x/6 = 1

(6x +5x)/30 =1

11x=30

x =30/11 or 2 8/11 hr

B). similerly

x/6 + x/7 =1

(7x+6x)/42 =1

7x+6x = 42

13x=42

x = 42/13 hrs

C).

x/10 + x/7 =1

(7x+10x)/70 =1

17x =70

x = 70/17 hr

D).

x/5 +x/9 =1

(9x +5x)/45=1

14x =45

x = 45/14 hours