15. Professor Rosseforp runs to work every day. On Thursday he ran $10 \%$ faster than his usual average speed. As a result, his journey time was reduced by $x$ minutes. How many minutes did the journey take on Wednesday?
A $11 x$
B $10 x$
C $9 x$
D $8 x$
E $5 x$
Solution: A
Suppose that the distance that Professor Rosseforp runs is $d$ and his usual average speed (in terms of the units used for distance and minutes) is $s$. So, on Wednesday his journey takes him $\frac{d}{s}$ minutes. On Thursday his average speed was $\frac{110}{100} s=\frac{11}{10} s$ and so the journey takes him $\frac{d}{\frac{11}{10} s}=\frac{10 d}{11 s}$ minutes. We therefore have $\frac{d}{s}-\frac{10 d}{11 s}=x$. This gives $\frac{d}{11 s}=x$ and hence $\frac{d}{s}=11 x$. So on Wednesday his journey took him $11 x$ minutes.