Mathematics 10 — Exercise 5.5 · Q6

Full question

Rashi paints a house alone in 6 days; with a helper he takes 4 days. Find the helper’s time alone.

Step-by-step solution

1. Use daily work rates: 1/6 + 1/x = 1/4.

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

   $$\frac{1}{6}+\frac{1}{x}=\frac{1}{4}$$

3. Multiply BOTH sides by the common denominator.

   $$\left(12\times x\right)\times \left(\frac{1}{6}+\frac{1}{x}\right)=\frac{12\times x}{4}$$

4. Expand the products.

   $$2\times x+12=3\times x$$

5. Equate the corresponding entries.

   $$2\times x+12=3\times x$$

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

   $$-x=0-12$$

7. Simplify the constant calculation.

   $$-x=-12$$

8. Divide both sides by the variable coefficient.

   $$x=-\frac{12}{-1}$$

9. Reduce the fraction.

   $$x=12$$

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

    $$\left\{12\right\}$$

Answer

The final answer is shown below.