Street Lamps
Walking up a steep hill, I pass 10 equally spaced street lamps. How long do I take to walk from the first lamp to the last?
Age
11 to 14
Challenge level
Problem
Walking up a steep hill, I pass 10 equally spaced street lamps.
I take 5 seconds to walk from the first lamp to the second lamp, 6 seconds from the second lamp to the third, and so on, with each time increasing by 1 second as I slow down.
How long do I take to walk from the first lamp to the last?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 81 seconds
You can count out 9 numbers and add them up:
Note that there are 9 gaps between the lamps, so the total time is
(5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13) seconds = 81 seconds.
Or use patterns:
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