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°.
