## Friday, August 01, 2008

### Friday Fun - Cycling on the Bridge

Two bicyclists start cycling from opposite ends of a bridge. One cyclist is faster than the other and they meet at a point 2,000 feet from the nearest end. When each cyclist reaches the opposite end of the bridge, he takes a 15 minute rest break and then starts on his on return trip. The cyclists again meet 720 feet from the other end. Assuming each is cycling at a constant speed, how long is the bridge?

Note: There is no mention of the actual speed of each cyclist, or the time that each takes but this problem is solvable. In fact, there is an elegant solution that could be understood by an elementary school student, with basic rules of addition and subtraction. It can also be solved the "hard" way. I'll post the elegant solution next week.

Edit: I've provided an answer in the comments.

#### 10 comments:

1. Well, I had to do it "the hard way" in order to work backwards to discover "the elegant way". Even the hard way was pretty mild though; just had to deal with 3 variables and a generous number of equations with which solve those 3 variables.

2. I think I may have the correct answer, but my math may be wrong. This problem makes me think of a Steven Wright joke.

3. If it is the joke about a map, then I think you have the right answer.

4. It is! Fantastic!

5. Good luck folding that map back up! :-)

6. might take me all summer

7. The Steven Wright quote is, "I have a map of the United States... actual size. It says, Scale: 1 mile = 1 mile. I spent last summer folding it."

Solution:
When they first meet, together they have travelled the full length of the bridge. They continue to the opposite ends, for a total of two bridge lengths. Finally they turn around and meet again for a total of 3 bridge lengths. On the first leg, the slower cyclist has gone 2,000 feet. So at the end he will have cycled three times this distance or 6,000 feet. Subtracting the 720 feet he has cycled on the return trip leaves a bridge length of 5,280 feet (or exactly 1 mile).

Answer:
The bridge is exactly 1 mile long.

8. "So at the end he will have cycled three times this distance or 6,000 feet."

I'm not sure I understand why we can multiply 2000 x 3. Can you explain this further....?

I definitely did it the "hard" way.

9. At the first meeting, together they went a distance of 1 bridge length. At the second meeting, together they went a distance of 3 bridge lengths. Thus the proportion cycled by each is 1 to 3.

10. (Slaps forehead) Duh...thanks Blaine

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