Multiple choice

Pipe A, open alone with a constant rate of flow, fills an empty tank in x hours. Pipe B, open alone with a constant rate of flow, empties a full tank in y hours, where x y. When both pipes are open, the tank becomes full in z hours, where 1 z = 1 x - 1 y . Which of the following expresses z in terms of x and y?

  1. y - x x y

  2. x y y - x

  3. x - y

  4. xy

  5. x 2 + y 2 x - y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From 1/z = 1/x - 1/y = (y - x)/(xy), taking reciprocals gives z = xy/(y - x). Option B matches this expression.

AI explanation

The given formula is 1/z = 1/x - 1/y, which is the standard work rate equation for one pipe filling and one pipe emptying a tank. To express z in terms of x and y, find a common denominator on the right side to get 1/z = (y - x)/(xy). Taking the reciprocal of both sides yields z = xy / (y - x). The result is xy / (y - x).

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