There is a straight road between town A and town B of length 130 km.
Maxi travels from town A to town B.
Pippa travels from town B to town A.
Both travel at a constant speed of 40 km/h.
Maxi leaves 30 minutes before Pippa.
Work out how far from town A they will be when they pass each other.
▶️ Answer/Explanation
Ans: 75 km
Maxi’s head start: 40 km/h × 0.5 h = 20 km
Remaining distance when Pippa starts: 130 – 20 = 110 km
Combined speed: 40 + 40 = 80 km/h
Time to meet: 110 ÷ 80 = 1.375 hours
Distance from A: 20 + (40 × 1.375) = 75 km
(a) Juan asks 40 people which language they speak at home.
The table shows the results.
| Language | Frequency | Pie chart sector angle |
|---|---|---|
| English | 18 | \(162^\circ\) |
| French | 11 | |
| Spanish | 7 | |
| Other | 4 |
Juan wants to draw a pie chart to show this information.
(i) Complete the table.
(ii) Complete the pie chart.
(b) Mansoor also asks some people which language they speak at home.
In Mansoor’s pie chart, the sector angle for Portuguese is \(108^\circ\).
Write down the fraction of these people who do not speak Portuguese at home.
▶️ Answer/Explanation
(a) (i) Ans: French: \(99^\circ\), Spanish: \(63^\circ\), Other: \(36^\circ\)
To find the sector angles:
- French: \(\frac{11}{40} \times 360^\circ = 99^\circ\)
- Spanish: \(\frac{7}{40} \times 360^\circ = 63^\circ\)
- Other: \(\frac{4}{40} \times 360^\circ = 36^\circ\)
(a) (ii) The pie chart should be completed with the calculated angles.
(b) Ans: \(\frac{252}{360}\) or simplified \(\frac{7}{10}\)
The fraction not speaking Portuguese is: \[ \frac{360^\circ – 108^\circ}{360^\circ} = \frac{252}{360} = \frac{7}{10} \]