10. On a training ride, Laura averages speeds of $12 \mathrm{~km} / \mathrm{h}$ for 5 minutes, then $15 \mathrm{~km} / \mathrm{h}$ for 10 minutes and finally $18 \mathrm{~km} / \mathrm{h}$ for 15 minutes.
What was her average speed over the whole ride?
A $13 \mathrm{~km} / \mathrm{h}$
B $14 \mathrm{~km} / \mathrm{h}$
C $15 \mathrm{~km} / \mathrm{h}$
D $16 \mathrm{~km} / \mathrm{h}$
E $17 \mathrm{~km} / \mathrm{h}$
Solution
D

To determine Laura's average speed over the whole ride we calculate the total distance she travels, and the total time that she takes.
Because 5 minutes is $\frac{1}{12}$ of an hour, Laura travels $\frac{1}{12} \times 12 \mathrm{~km}=1 \mathrm{~km}$ when she travels for 5 minutes at $12 \mathrm{~km} / \mathrm{h}$.
Because 10 minutes is $\frac{1}{6}$ of an hour, Laura travels $\frac{1}{6} \times 15 \mathrm{~km}=2.5 \mathrm{~km}$ when she travels for 10 minutes at $15 \mathrm{~km} / \mathrm{h}$.
Because 15 minutes is $\frac{1}{4}$ of an hour, Laura travels $\frac{1}{4} \times 18 \mathrm{~km}=4.5 \mathrm{~km}$ when she travels for 15 minutes at $18 \mathrm{~km} / \mathrm{h}$.

Therefore Laura travels at total of $1 \mathrm{~km}+2.5 \mathrm{~km}+4.5 \mathrm{~km}=8 \mathrm{~km}$ in $5+10+15$ minutes, that is, in 30 minutes, which is half an hour.

Because Laura travels $8 \mathrm{~km}$ in half an hour, her average speed is $16 \mathrm{~km} / \mathrm{h}$.