Mathematics 10 — Exercise 5.5 · Q5

Full question

Two cars 240 km apart travel towards each other at x and x+10 km/h and meet after 2 hours. Find both speeds.

Step-by-step solution

1. Each car travels speed×2 hours. Their distances add to 240 km.

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

   $$4\times x+20=240$$

3. Multiply BOTH sides by the common denominator.

   $$4\times x+20=1\times 240$$

4. Expand the products.

   $$4\times x+20=240$$

5. Equate the corresponding entries.

   $$4\times x+20=240$$

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

   $$4\times x=240-20$$

7. Simplify the constant calculation.

   $$4\times x=220$$

8. Divide both sides by the variable coefficient.

   $$x=\frac{220}{4}$$

9. Reduce the fraction.

   $$x=55$$

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

    $$\left\{55\right\}$$

11. The first speed is 55 km/h; add 10 for the other: 55+10=65 km/h.

Answer

The final answer is shown below.