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4024/21 May/Jun 2024, Question 9: Speed, Distance and Time

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Using two ports' bearings and distances from A, find a reverse bearing, a side length BC, and compare two boats' speeds over the same route.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Find the bearing of port A as seen from port B, given B's bearing from A is 107°.

  1. 1107 + 180 = 287°

Answer287

Part (b) · 4 marks

Calculate the distance BC using AB = 176 km, AC = 132 km and the angle at A between them.

  1. 1Angle CAB = 192 − 107 = 85°
  2. 2BC² = 176² + 132² − 2 × 176 × 132 × cos 85°
  3. 3BC² = 48 400 − 4049.6… = 44 350.4…
  4. 4BC = 210.59… ≈ 211 km

Answer211 or 210.5 to 210.6

Part (c) · 5 marks

Boat B travels BA at 48 km/h from 10.00 am; boat C travels CA arriving 7 minutes earlier, having left at 10.15 am. Find C's average speed.

  1. 1Boat B: 176 ÷ 48 = 3 2/3 h = 3 h 40 min, arrives 1.40 pm
  2. 2Boat C arrives 7 min earlier: 1.33 pm
  3. 3Boat C time = 10.15 am to 1.33 pm = 3 h 18 min = 3.3 h
  4. 4Speed = 132 ÷ 3.3 = 40 km/h

Answer40

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