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.)

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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

60t = 40(t + 1/6)
60t = 40t + 40/6
360t = 240t + 40
120t = 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.

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