Question

Car travels $xkm$ for every litre of petrol, while car $B$ travels $(x+1)km$ for every litre of petrol.
(i) Write down the number of petrol used by car $A$ and $B$ in covering a distance of $400km$.
(ii) If car $A$ used $4$ litre of petrol more than car $B$ in covering $400km$, write down an equation in solve it to determine the number litres of petrol used by car $B$ for the journey.

Answer 1

$A\to x$ km in 1 lt $\Rightarrow 1$ km $\to \frac{1}{x}$ lt petrol

$B\to (x+1)$ km in 1 lt $\Rightarrow 1$ km $\to \frac{1}{x+1}$ lt petrol

(i) for 400 km : A $\Rightarrow 400$ km $\to \frac{400}{x}$ lt of petrol

$B\Rightarrow 400$ km $\to \frac{400}{x+1}$ lt of petrol

(ii) $A=B+4$ lt $\Rightarrow \frac{400}{x}=\frac{400}{x+1}+4\Rightarrow 400(x+1)=400x+4x(x+1)$

$\Rightarrow 400x+400=400x+4x^2+4x\Rightarrow 4x^{2}4x-400=0$

$x^2+x-100=0$ $x=\frac{-1\pm \sqrt{1+4\times 100}}{2}=\frac{-1\pm \sqrt{401}}{2}$ lt.