Mathematics 10 — Exercise 5.5 · Q2

Full question

Arshia and Ibraheem finish a job in 4 hours together. Arshia alone takes 6 hours. How long does Ibraheem take alone?

Step-by-step solution

1. Let Ibraheem’s time be x hours. One-hour work rates are 1/6 and 1/x; together they do 1/4 of the job per hour.

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.