Average Speed

QUESTION:

A motorist wishes to travel 40 kilometers at an average speed of 40 km per hour. During the first 20 kilometers, an average speed of 40 km/h is maintained. During the next 10 kilometers, however, the motorist goofs off and averages only 20 km/h. To drive the last 10 kilometers and average 40 km/h, the motorist must drive

60 km/h.
80 km/h.
90 km/h.
faster than the speed of light.

drawing of the problem described

ANSWER: D

You would have to travel at an infinite speed and finish the last 10 kilometers in zero time to attain an average speed of 40 km/h! Why? Because you have one hour to make the trip, and your one hour is up at the 30-kilometer point. You spent 1/2 hour getting to the half-way point (20 kilometers) and another 1/2 hour when you averaged 20 km/h over that 10-kilometer stretch. So you'd have to cover the entire 40 kilometers in one hour—that means, the last kilometers must be driven in no time at all!

Be careful in averaging speeds like you average distances. Speed involves distance and time. Be sure to consider time in problems that involve speed!

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