Higher June 2023 Paper 1 Q27
27 A journey has two stages.
| Distance (km) | Average speed (km/h) | Time (h) | |
|---|---|---|---|
| Stage 1 | 30 | \(a\) | \(\dfrac{30}{a}\) |
| Stage 2 | 30 | \(b\) | \(\dfrac{30}{b}\) |
Show that the average speed for the whole journey, in km/h, is \(\quad \dfrac{2ab}{a + b}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| (Total time \(=\)) \(\dfrac{30}{a} + \dfrac{30}{b}\) | M1 | oe eg \(\dfrac{30b}{ab} + \dfrac{30a}{ab}\) or \(\dfrac{30(b + a)}{ab}\) |
| correct expression for total distance \(\div\) total time | M1dep | eg \((30 + 30) \div \left(\dfrac{30}{a} + \dfrac{30}{b}\right)\) or \(60 \div \dfrac{30(b + a)}{ab}\) or \(60 \times \dfrac{ab}{30(b + a)}\) |
| \(60 \times \dfrac{ab}{30(a + b)} = \dfrac{2ab}{a + b}\) | A1 | condone \(b + a\) for \(a + b\) condone \(30a + 30b\) for \(30(a + b)\) |
Additional guidance
| Students can gain M1M1 if they incorrectly simplify a correct expression for total time before forming the division eg \(\dfrac{30}{a} + \dfrac{30}{b} = \dfrac{60}{a + b}\) followed by \(60 \div \dfrac{60}{a + b}\) | M1M1A0 |
| Allow correct cancellation of 60 and 30 at any stage of the working |