Variation Questions

Question

1. The number of hours required to build a fence is inversely proportional to the number of people working on the fence. If it takes 2 people, 99 hours to complete the fence, then how long will it take 19 people to build the fence? (round answer to 2 decimal places if needed)

 

2. Wind resistance is jointly proportional to velocity and surface area of the object. If an object is traveling 5 mph and has a surface area of 41 square feet it will experience a wind resistance of 46.125 Newtons. How fast must an object be moving to experience a wind resistance of 153.9 Newtons if it has a surface area of 57 square feet?

 

3. The weekly pay that Sarah receives varies directly with the number of hours she works. If she works 36 hours she makes 448.2. How much money would she make if she works 25 hours?

Answer 1

1. Let h = number of hours and p = number of people

 

    Then, h = k/p, for some number, k

 

    Since h = 99 when p = 2, 99 = k/2.  So, k = 198

 

    Therefore, h = 198/p

 

    So, if p = 19, h = 198/19 = 10.42 hours

 

2. Let r = wind resistance, v = velocity, s = surface area

 

    Then, r = kvs   Since r = 46.125 when v = 5 and s = 41, 

 

            46.125 = k(5)(41)    So, k = 0.225

 

     r = 0.225vs

 

     When r = 153.9 and s = 57, 153.9 = 0.225v(57)

 

                                                  v = 12 mph

 

3. Let w = weekly pay and h = number of hours

 

    Then, w = kh

 

    Since w = 448.2 when h = 36, 448.2 = 36k.

 

                                                    k = 12.45

 

    w = 12.45h

 

    When h = 25, w = 12.45(25) = 311.25