Two taps fill a tank. Working alone, the times they take (in hours) are the two zeroes of x² − 12x + 27. In one hour the first tap fills 1/α of the tank and the second fills 1/β. What fraction of the tank do the two taps fill together in one hour?

Question

Accepted Answer

4/9. 1/ + 1/ = + / = 12/27 = 4/9 of the tank per hour. (The zeroes are 3 h and 9 h, and 1/3 + 1/9 = 4/9 .) 9/4 inverts the fraction; 1/12 uses 1/ + ; 1/27 uses 1/ .

Two taps fill a tank. Working alone, the times they take (in hours) are the two zeroes of $x^{2} - 12 x + 27$ .
In one hour the first tap fills 1/α of the tank and the second fills 1/β.
What fraction of the tank do the two taps fill together in one hour?

Step-by-Step Solution

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More Class 10 Zeroes and Coefficients practice

Two taps fill a tank. Working alone, the times they take (in hours) are the two zeroes of x2−12x+27.In one hour the first tap fills 1/α of the tank and the second fills 1/β.What fraction of the tank do the two taps fill together in one hour?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Zeroes and Coefficients practice

Two taps fill a tank. Working alone, the times they take (in hours) are the two zeroes of $x^{2} - 12 x + 27$ .
In one hour the first tap fills 1/α of the tank and the second fills 1/β.
What fraction of the tank do the two taps fill together in one hour?