Solving rational equations and inequalities help

Question

1.) Sarah can mow a lawn in 3 hours. Richard needs 6 hours to do the same work. How long will it take them if they work together?
2.) Zainab can make and decorate a wedding cake in 20 hours, working alone. Nanting can do the same work in 30 hours. How long will it take Zainab and Nanting to complete the cake if they work together?
3.) Megan can see a quilt in 8 days, Tyler in 5 days and Kate in 3 days. If all three work together, how long will it take them to do the work. Round answer to nearest tenth.
4.) Brandon's construction company can build a skyscraper in 6 months. If Carter's construction company helps him, they can build the skyscraper in 4 months. How long would it take Carter's construction company to build the skyscraper alone?
5.) It takes Max 5 hours to pick a bushel of blueberries. If Ryan helps him it will take 3 hours. How long would it take Ryan alone?
6.) Brittany, kristi and Tom can prepare the ballots for homecoming in 2 hours. If Brittany could prepare them in 5 hours and kristi in 6 hours, how long will it take tom to prepare the ballots by himself? Round answer to nearest tenth.
7.) A river barge travels at an average 8 mph in still water. The barge travels 60 miles up the Mississippi River and 60 miles down the river a total of 16.5 hours. What is the average speed of the current in this part of the river? Round to the nearest tenth.

Answer 1

1)

 

X - number of hours work together

 

1/ 3 + 1/6 = 1/X

 

  2/6 + 1/6 = 1/X

 

  1/2 = 1/X

 

  X = 2

 

You can follow the same suit, and do 2-6

 

7)

 

     SS - speed at Still water = 8m/hr

     Sc - average speed of the current

      Use the Distance formula   d = s .t    t = d/s

 

     60        +  60        = 16.5  

     8 - Sc       8 + Sc

 

     Solve this equation for Sc