Mathematics 10 — Exercise 5.5 · Q8

Full question

Fahad runs 600 m at speed x, then 600 m at twice that speed. The printed question gives total time “2½” but omits its unit. Find the starting speed.

Step-by-step solution

1. The printed statement omits the time unit. If 2½ means minutes, convert to (5/2)×60=150 seconds.

2. Add the two times: 600/x + 600/(2x) = 150.

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

   $$\frac{900}{x}=150$$

4. Multiply BOTH sides by the common denominator.

   $$\left(\frac{900}{x}\right)\times x=150\times x$$

5. Expand the products.

   $$900=150\times x$$

6. Equate the corresponding entries.

   $$900=150\times x$$

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

   $$-150\times x=0-900$$

8. Simplify the constant calculation.

   $$-150\times x=-900$$

9. Divide both sides by the variable coefficient.

   $$x=-\frac{900}{-150}$$

10. Reduce the fraction.

    $$x=6$$

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

    $$\left\{6\right\}$$

12. Under the minutes assumption the speed is 6 m/s. If the stated time instead means 2½ seconds, the same calculation gives 360 m/s; the missing unit must be clarified.

Answer

The final answer is shown below.