2440.12 – Orthodontist

Phoebe Beebe has an appointment with her orthodontist Dr. Jane Pullem (and nurse Willy Fillem) at 2:55 this afternoon. Her brother Led will drive her there, and they will leave right after school. If they go 60 kph (about 35 mph) the whole way, they will arrive 5 minutes early. But if they drive 40 kph (about 25 mph) the whole way, they will arrive 5 minutes late. What time does school get out, and how far do they have to drive?

Solution

Consider the chart shown below. We'll use $d = r \cdot t$ , where $d$ is the distance to the orthodontist's office in kilometers,

and $t$ is the time in hours that it takes to drive the distance at $60$ kph. Since $d = d$ , we have

\begin{aligned} 60t &=& 40(t + 1/6) \\ 60t &=& 40t + 40/6 \\ 360t &=& 240t + 40 \\ 120t &=& 40 \\ t &=& 40/120 = 1/3 \text{ hour.} \end{aligned}

At $60$ kph they drive for $20$ minutes and arrive $5$ minutes early, at 2:50. So they left at 2:30, the time that school got out. The distance is $60 \cdot \frac{1}{3} = 20$ km.