18. Marc always cycles at the same speed and he always walks at the same speed. He can cover the round trip from his home to school and back again in 20 minutes when he cycles and in 60 minutes when he walks. Yesterday Marc started cycling to school but stopped and left his bike at Eva's house on the way before finishing his journey on foot. On the way back, he walked to Eva's house, collected his bike and then cycled the rest of the way home. His total travel time was 52 minutes.
What fraction of his journey did Marc make by bike?
A $\frac{1}{6}$
B $\frac{1}{5}$
C $\frac{1}{4}$
D $\frac{1}{3}$
E $\frac{1}{2}$
SOlUTION
B

Let the fraction of his journey that Marc cycles be $k$. Therefore, the time he spends cycling is $20 k$ and the time he spends walking is $60(1-k)$. Since the total time he takes is 52 minutes, we have $52=20 k+60(1-k)$ and hence $52=20 k+60-60 k$. This simplifies to $8=40 k$ which has solution $k=\frac{1}{5}$.