WAEC 2021 · Paper 2 · Q8

(a)
The time ( $T$ ) spent on erecting a concrete pillar is partly constant and partly varies as three times the base area ( $A$ ). If it took 27 hours to erect a pillar with a base area of $24\text{ m}^2$ and 52 hours for a pillar with a base area of $48\text{ m}^2$ , find the time taken to erect a pillar with base area $60\text{ m}^2$ .

Worked solution (try it first)

"Partly constant and partly varies as three times the base area": $T = a + b(3A) = a + 3bA$ , with $T$ in hours and $A$ in m².
$A = 24$ , $T = 27$ : $a + 72b = 27$ .
$A = 48$ , $T = 52$ : $a + 144b = 52$ .
Subtract: $72b = 25$ , so $b = \frac{25}{72}$ .
Then $a = 27 - 72 \times \frac{25}{72}$
$= 27 - 25$
$= 2$ .
So $T = 2 + 3 \times \frac{25}{72}A$
$= 2 + \frac{25}{24}A$ .
For $A = 60$ : $T = 2 + \frac{25}{24} \times 60$
$= 2 + 62\frac12$
$= 64\frac12$ hours.