Mathematics 10 — Exercise 5.5 · Q4

Full question

Huria alone completes a project in 12 hours; with Abdul Hadi they finish in 5 hours. Find Abdul Hadi’s time alone.

Step-by-step solution

1. Let Abdul Hadi’s time be x. Add one-hour work rates to get the combined rate.

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

   $$\frac{1}{12}+\frac{1}{x}=\frac{1}{5}$$

3. Multiply BOTH sides by the common denominator.

   $$\left(60\times x\right)\times \left(\frac{1}{12}+\frac{1}{x}\right)=\frac{60\times x}{5}$$

4. Expand the products.

   $$5\times x+60=12\times x$$

5. Equate the corresponding entries.

   $$5\times x+60=12\times x$$

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

   $$-7\times x=0-60$$

7. Simplify the constant calculation.

   $$-7\times x=-60$$

8. Divide both sides by the variable coefficient.

   $$x=-\frac{60}{-7}$$

9. Reduce the fraction.

   $$x=\frac{60}{7}$$

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

    $$\left\{\frac{60}{7}\right\}$$

Answer

The final answer is shown below.