### Brain Teasers

# Susan's Trip

Susan starts at point A, walks 15 feet in one direction, makes a 90 degree turn to the left, walks 20 feet, walks in a perfect circle around point A, and takes the same path she took leaving point A, until she is back at point A. Assuming she walks at a constant rate of 4 feet per second, makes no stops until she arrives at point A again, and that we do not consider acceleration, how long is her entire trip (rounded to the nearest second)?

### Answer

57 seconds.First off, the formula of Speed = Distance / Time can be rewritten as Time = Distance / Speed. (On both sides of the equation we can multiply by Time and divide by Speed.) We will need this equation later.

We know Susan travels 15 feet in one direction and 20 feet in another and does this again on her return trip. Using the Pythagorean Theorem we find that the radius of the circle is 25 feet; therefore, the diameter is 50 feet and the circumference is about 157.1 feet. We can then plug all our values into the equation (units in feet cancel out, leaving seconds):

Time = (15 ft. + 20 ft. + 157.1 ft. + 20 ft. + 15 ft.) / (4 ft. per second) = 57 seconds (rounded to the nearest second).

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