Challenge question #39 (05/12/2016)
Junior Question
A motorist, after having his car overhauled, finds that he can travel an additional $5$ km per litre of petrol. He is now using $2$ litres less for a journey of $200$ km than previously.
How many km per litre was he getting previously?
The motorist was previously getting $20$ km per litre of petrol.
Worked SolutionSuppose the car was originally travelling $x$ km per L before the overhaul.
So, it travels $(x+5)$ km per L after the overhaul.
The journey of $200$ km required $\footnotesize\dfrac{200}{x}$ L of petrol before the overhaul, and $\footnotesize\dfrac{200}{(x+5)}$ L afterwards.
Thus the motorist was previously getting $20$ km per litre of petrol.
Senior Question
Suppose $a+b=1$ and $a^{2}+b^{2}=3$.
Find the value of $a^{5}+b^{5}$.
$a^{5}+b^{5}=11$
Worked Solution