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 Math Help > Math Puzzles > 2004 State Logic Quiz > Question 12 > Question 12

# Academic Decathlon 2004 State Championship Logic Quiz

## Question 12

A bicyclist starts his ride home from a point 10 miles away from his house, going 5 miles per hour (assume the road is a perfect straight line).  At the same time, a frog, initially sitting on his helmet (always wear your helmet!) takes off and hops toward the house at 15 miles per hour.  Upon reaching the house, the frog turns right around and hops back toward the bicyclist.  When it reaches him, it turns around again and hops back to the house.  The frog keeps doing this until the man finally arrives at the house himself.  By the time he reached home, how many miles did the frog leap?

### Answer:

30 miles.

Although the path taken by the frog has a lot of twists and turns in it, the frog's speed remains constant -- 15 miles an hour, the whole time.  So the question is easily solved by determining the amount of time the frog spent hopping, and then multiplying it by the frog's speed to get the distance it hopped.

Since the frog began hopping at the same time the bicyclist began riding, and the bicyclist took two hours to go 10 miles at 5 miles per hour, it follows that the frog spent the same two hours hopping.

2 hours times 15 miles per hour equals 30 miles.

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