Bayside, Millwater and Westbridge are towns beside a lake.
The scale drawing shows the positions of Bayside (B) and Millwater (M).
The scale is 1 centimetre represents 2 kilometres.
(i) Find the actual distance between Bayside and Millwater.
(ii) Westbridge (W) is 17 km from Bayside on a bearing of 155°.
On the scale drawing, mark the position of Westbridge.
(b) (i) A boat travels from Bayside to Westbridge.
The table gives some information about its journey.
Work out how long the boat takes to travel from Millwater to Westbridge. Give your answer in hours and minutes.
(ii) The boat returns directly to Bayside.
It takes 1 hour 20 minutes to travel the 17 km.
Work out the average speed of this journey.
(c) Here are the ticket prices for a boat trip from Bayside to Westbridge.
(i) Calculate the cost per person for a group of 15 people.
(ii) A group of 24 people buy tickets for the boat trip from Bayside to Westbridge.
Calculate the least amount of money the group needs to pay.
▶️ Answer/Explanation
(a)(i) 9 km
Measure distance on scale drawing (4.5 cm) and multiply by scale factor (2 km/cm).
(a)(ii) W marked at correct position
Convert 17 km to 8.5 cm on drawing. Draw bearing of 155° from B and mark W.
(b)(i) 1 hour 22 minutes
Subtract departure time from Millwater (11:45) from arrival time at Westbridge (13:07).
(b)(ii) 12.75 km/h
Convert 1 hour 20 minutes to 4/3 hours. Speed = Distance/Time = 17 ÷ (4/3).
(c)(i) $9.25
Divide group cost ($138.75) by number of people (15).
(c)(ii) $225.45
Optimal combination: 1 group of 15 ($138.75), 1 group of 6 ($57.30), and 3 individuals ($29.40).
Point B is 36km from point A on a bearing of 140°.
(a) Using a scale of 1 centimetre to represent 4 kilometres, mark the position of B.

(b) (i) Point C is 28 km from A and 20km from B. The bearing of C from A is less than 140°. Using a ruler and compasses only, construct triangle ABC. Show all your construction arcs.
(ii) Measure angle ACB.
▶️ Answer/Explanation
- For (a): Convert 36km to 9cm (scale 1cm=4km). Draw point B 9cm from A at 140° bearing.
- For (b)(i): Draw 7cm arc (28km) from A and 5cm arc (20km) from B. Their intersection is C.
- For (b)(ii): Measure angle at C using protractor. Should be 38°-42°.