Mathematics 10 — Exercise 5.5 · Q3

Full question

One pipe fills a tank in 5 hours, another in 8 hours. The second closes after 2 hours. Find total filling time.

Step-by-step solution

1. Let total time be x. Pipe 1 runs x hours and fills x/5; pipe 2 runs only 2 hours and fills 2/8. These fractions total one tank.

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

   $$\frac{x}{5}+\frac{1}{4}=1$$

3. Multiply BOTH sides by the common denominator.

   $$20\times \left(\frac{x}{5}+\frac{1}{4}\right)=20\times 1$$

4. Expand the products.

   $$4\times x+5=20$$

5. Equate the corresponding entries.

   $$4\times x+5=20$$

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

   $$4\times x=20-5$$

7. Simplify the constant calculation.

   $$4\times x=15$$

8. Divide both sides by the variable coefficient.

   $$x=\frac{15}{4}$$

9. Reduce the fraction.

   $$x=\frac{15}{4}$$

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

    $$\left\{\frac{15}{4}\right\}$$

Answer

The final answer is shown below.