Mathematics 10 — Exercise Review · Q6

Full question

Two taps fill a tank in 6 and 9 hours separately. Find time to fill it together.

Step-by-step solution

1. In x hours they fill x/6 and x/9 tanks; the sum must be one tank.

2. Translate the stated rates/times into this equation.

   $$\frac{5\times x}{18}=1$$

3. Multiply BOTH sides by the common denominator.

   $$18\times \left(\frac{5}{18}\right)\times x=18\times 1$$

4. Expand the products.

   $$5\times x=18$$

5. Equate the corresponding entries.

   $$5\times x=18$$

6. Collect the variable terms on the left and constants on the right.

   $$5\times x=18+0$$

7. Simplify the constant calculation.

   $$5\times x=18$$

8. Divide both sides by the variable coefficient.

   $$x=\frac{18}{5}$$

9. Reduce the fraction.

   $$x=\frac{18}{5}$$

10. Reject any negative time, speed or quantity; keep the physically valid value.

    $$\left\{\frac{18}{5}\right\}$$

Answer

The final answer is shown below.