Mathematics 10 — Exercise 5.5 · Q7

Full question

Ishmal runs 10 km in 2x/(x+4) hours at 8 km/h. Find x.

Step-by-step solution

1. Required time is distance/speed = 10/8 hours. Equate it to the given time expression.

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

   $$\frac{2\times x}{x+4}=\frac{5}{4}$$

3. Multiply BOTH sides by the common denominator.

   $$\left(\frac{2\times x}{x+4}\right)\times \left(4\times x+16\right)=\frac{20\times x+80}{4}$$

4. Expand the products.

   $$8\times x=5\times x+20$$

5. Equate the corresponding entries.

   $$8\times x=5\times x+20$$

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

   $$3\times x=20+0$$

7. Simplify the constant calculation.

   $$3\times x=20$$

8. Divide both sides by the variable coefficient.

   $$x=\frac{20}{3}$$

9. Reduce the fraction.

   $$x=\frac{20}{3}$$

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

    $$\left\{\frac{20}{3}\right\}$$

Answer

The final answer is shown below.