Question

You and a friend both leave the same restaurant to drive home. You are heading directly west at 30 miles per hour and he or she is heading directly south at 40 miles per hour. After half an hour, how fast (in mph) is the distance between you changing? Do not include units in your answer.

Answer 1

50

Explanation:

The distance between the friends is changing at the constant rate of 50 mph.

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The equation for the distance in the westerly direction is ...

w = 30t . . . . . miles, where t is time in hours

The equation for the distance in the southerly direction is ...

s = 40t . . . . . miles, where t is time in hours

Then the total distance between the friends is ...

d = √((30t)² + (40t)²) = √(2500t²) = 50t . . . . miles, where t is time in hours

And the rate of change of distance is the derivative of this with respect to t:

dd/dt = 50 . . . . . . miles per hour