WAEC 2014 · Paper 2 · Q3

Linear & simultaneous equations

(a)
Solve the simultaneous equations $\dfrac1x + \dfrac1y = 5$ and $\dfrac1y - \dfrac1x = 1$ .
Separate values with commas, e.g. 3, −2
(b)
A man drives from Ibadan to Oyo, a distance of $48\text{ km}$ , in 45 minutes. If he drives at $72\text{ km/h}$ where the surface is good and $48\text{ km/h}$ where it is bad, find the number of kilometres of good surface.

Worked solution (try it first)

(a)

Treat $\frac1x$ and $\frac1y$ as the unknowns.
Adding the equations, the $\frac1x$ terms cancel: $\frac2y = 6$ , so $\frac1y = 3$ and $y = \frac13$ .
Taking the second equation from the first: $\frac2x = 4$ , so $\frac1x = 2$ and $x = \frac12$ .

(b)

Let the good surface be $x$ km.
The bad surface is then $(48 - x)$ km.
Time $= \frac{\text{distance}}{\text{speed}}$ , so the two times are $\frac{x}{72}$ and $\frac{48 - x}{48}$ hours.
The whole journey takes 45 minutes $= \frac34$ hour: $\frac{x}{72} + \frac{48 - x}{48} = \frac34$ .
Multiply every term by 144: $2x + 3(48 - x) = 108$ .
So $2x + 144 - 3x = 108$ , $-x = -36$ and $x = 36$ .
There are 36 km of good surface.

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