2024 Mathematics WAEC (WASSCE) Essay Past Questions (Paper 2)

Question 1

The time (t) taken to buy fuel at a filling 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 the;

(a) relationship between t, P, and V;

Solution

t \(\scriptsize \propto \normalsize \frac{V}{P}\)

introducting constant k

t = \(  \frac{kV}{P}\)

Given P = 5, t = 10 min, V = 20

t = \(  \frac{kV}{P}\)

k = \(  \frac{Pt}{V}\)

k = \(  \frac{5 \: \times \: 10}{20}\)

k = \(  \frac{50}{20}\)

k = \(  \frac{5}{2}\)

relationship between t, P, and V

t = \(  \frac{\frac{5}{2}V}{P}\)

t = \(  \frac{5V}{2P}\)

(b) time it takes to fuel 50 vehicles at a station with 2 pumps;

Solution

t = ?, V = 50, P = 2

t = \(  \frac{5 \: \times \: 50}{2\: \times \: 2} \\ = \frac{250}{4}  \\ \scriptsize = 62.5\: mins\)

(c) number of pumps required to fuel 40 vehicles in 20 minutes.

Solution

t = 20 min, V = 40, P = ?

P = \(  \frac{5\: \times \: 40}{2\: \times \: 20}\\\scriptsize = 5 \: pumps\)