B1. John walks from home to school with a constant speed, and his sister Joan bikes twice as fast. The distance between their home and school is $3 \mathrm{~km}$. If Joan leaves home 15 minutes after John then they arrive to school at the same time. What is the walking speed (in $\mathrm{km} / \mathrm{h}$ ) of John?
Solution 1: Let $x(\mathrm{~km} / \mathrm{h})$ be the speed of John. Then the speed of Joan is $2 x$. The time John spends for walking to school is $3 / x$ hours. The time Joan spends for biking to school is $3 /(2 x)$ hours. Since she leaves home $0.25 \mathrm{~h}$ after John and arrives to school at the same time, we have the equation: $3 / x=0.25+3 /(2 x)$. Solving it we find $x=6 \mathrm{~km} / \mathrm{h}$.
Solution 2: Joan covers twice the distance as John in the same time, so to arrive together Joan must leave when John is halfway. Thus John has walked $1.5 \mathrm{~km}$ in 15 minutes, or $1 / 4$ hour. John therefore walks $4 \times 1.5=6 \mathrm{~km} / \mathrm{hr}$.
Answer: 6 .