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Questions › DSE › DSE 2014 › Q28
2 marks, −0.666666666666667Mathematics › Single-variable optimisation › Applied optimisationHardabout 3 min

DSE 2014 Question 28: Single-variable optimisation

Sania's boat is at point AAA; the closest point on land, BBB, is 2 km away, and CCC on land is 6 km from BBB with triangle ABCABCABC right-angled at BBB. She rows to a point PPP on BCBCBC then jogs to CCC. She rows at 2 km/hr and jogs at 5 km/hr. At what distance from BBB should she choose PPP to minimise her time to CCC?

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Sania's boat is at point A; the closest point on land, B, is 2 km away, and C on land is 6 km from B with triangle ABC right-angled at B. She rows to a point P on BC then jogs to C. She rows at 2 km/hr and jogs at 5 km/hr. At what distance from B should she choose P to minimise her time to C? (A) 21/√4 (B) 4/√21 (C) 4/√12 (D) 21/√21

Single-variable optimisation has come up 37 times in 6 exams since 2010.

What this question tests

This question is on Applied optimisation, part of Single-variable optimisation in Mathematics.

Maximising profit, revenue or area and minimising cost or time in applied settings.

TestStop has 12 past-paper questions on this subtopic.

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Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.