WAEC 2024 · Paper 2 · Q1

Variation

The time ( $t$ ) taken to buy fuel at a filling station varies directly as the number of vehicles ( $V$ ) in a queue and inversely as the number of pumps ( $P$ ) available at the station. At a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find the:

(a)
relationship between $t$ , $P$ and $V$ ( $t$ in terms of $V$ and $P$ );
(b)
time it takes to fuel 50 vehicles at a station with 2 pumps (minutes);
(c)
number of pumps required to fuel 40 vehicles in 20 minutes.

Worked solution (try it first)

(a)

$t$ varies directly as $V$ (on top) and inversely as $P$ (underneath): $t = \dfrac{kV}{P}$ .
With 5 pumps, 20 vehicles took 10 minutes: $10 = \dfrac{20k}{5} = 4k$ , so $k = \frac52$ .
The relationship is $t = \dfrac{5V}{2P}$ .

(b)

$V = 50$ , $P = 2$ : $t = \dfrac{5 \times 50}{2 \times 2}$
$= \dfrac{250}{4}$
$= 62.5$ minutes.

(c)

$t = 20$ , $V = 40$ : $20 = \dfrac{5 \times 40}{2P}$
$= \dfrac{100}{P}$ , so $P = \dfrac{100}{20} = 5$ pumps.

Report a problem with this question