Problem 21 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
Logic & Word Problems
perimeterspatial-reasoning
In each of the four corners of a swimming pool, 10 m wide by 25 m long, there is a child. The swim instructor is sitting almost in the middle of one of the long edges of the pool. When he calls the children, they all choose the longest path along the edges to reach him. What was the sum of the distances covered by the four children?
Show answer
Answer: E — 210 m
Show hints
Hint 1 of 2
The pool's perimeter is 2×(10+25) = 70 m; the instructor sits near the middle of a long edge.
Still stuck? Show hint 2 →
Hint 2 of 2
Each child walks the longer way round, which is 70 minus the short way; add the four long routes.
Show solution
Approach: use the perimeter and take the long way each time
- Perimeter = 2 × (10 + 25) = 70 m, with the instructor about 12.5 m from each end of a long edge.
- The two near corners take the long route 70 − 12.5 = 57.5 m each; the two far corners take 70 − 22.5 = 47.5 m each.
- Sum = 57.5 + 57.5 + 47.5 + 47.5 = 210 m.
- The total is 210 m, choice E.
Mark:
· log in to save