Question

SECTION A [40 marks] — Answer all questions in this section.
1. The time (t) taken to buy fuel at a station varies directly as the number of vehicles (V) in a queue and varies inversely as the number of pumps (P) available at the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find:
(a) the relationship between t, P and V;
(b) the time it takes to fuel 50 vehicles at a station with 2 pumps;
(c) the number of pumps required to fuel 40 vehicles in 20 minutes.

Accepted Answer

t ∝ V/P → t = kV/P.
Given P=5, V=20, t=10: 10 = k(20)/5 = 4k → k = 2.5.
(a) Relationship: t = 2.5V/P.
(b) At V=50, P=2: t = 2.5×50/2 = 62.5 minutes.
(c) At t=20 minutes, V=40, find P: 20 = 2.5×40/P = 100/P → P = 100/20 = 5 pumps.

GCE Mathematics 2024 Theory — Question 1

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