Phoebe Beebe has an appointment with her orthodontist 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? (The orthodontist’s name is Dr. Larry Filler; his nurse is Jane Pullam.)

We’ll use *d* = *rt*. Let’s make a chart.

d |
r |
t |

d |
60 | t |

d |
40 | t + 1/6 |

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

*t*= 40(

*t*+ 1/6)

60

*t*= 40

*t*+ 40/6

360

*t*= 240

*t*+ 40

120

*t*= 40

*t*= 40/120 = 1/3 hour

At 60 kph they drive for 20 minutes and arrive 5 minutes early, at 2:50 pm. So they left at 2:30, the time that school gets out. The distance is 60 · 1/3 = 20 km.