Direct, Inverse and Joint Variation

Determine the type of variation.

• Direct

• Inverse

• None

The frequency of a vibrating string varies inversely as its length. A string 3 feet long vibrates 175 cycles per

second. Find the frequency of a 5 foot string.

• 105 cycles

• 291.7 cycles

• 2625 cycles

• 332 cycles

The time required to process a shipment of goods at Wal-Mart varies directly with the number of items in the

shipment and inversely with the number of workers assigned. If 15,000 items can be processed by 8 workers in 10 hours, then how long would it take 12 workers to process 20,000 items?

• 6.5 hours

• 7.75 hours

• 8.9 hours

• 10.2 hours

The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the

velocity. If a wind blowing at 50 mph exerts a force of 75 pounds on a surface of 500 ft², how much force will a

wind of 75 mph place on a surface of 10 ft²?

• 2.25 pounds

• 3.375 pounds

• 0.67 pounds

• 1 pound

Suppose y varies directly as x, and y=39 when x=3.  Find the value of y when x=2.

• 26

• 3

• 58.5

• 2

Suppose p varies directly as r, and p varies inversely as t.
t = 20 when p = 4 and r = 2.
Find t when r = 10 and p = -5.

• 80

• -80

• 4

• -20

Suppose a varies jointly as b & c. 
If a = 15 when b = 4
and c = 5,
then find b when a = 60 and c = 5.

• 320

• 225

• 16

• 8

Suppose j varies inversely with m.
If j = 60 when m = 0.3 , find j when m = -2

• -9

• 9

• 400

• -400

Suppose f varies directly as g, and f varies inversely as h.
f = -12 when h = 4 and g = -3.
Find g when f = 28 and h = 8.

• 14

• -14

• 16

• -16

Is the given table a direct variation? If so, what is the constant of variation?

• Yes; 1/3

• Yes; 3

• Yes; 5

• No