Problem 15 · 2018 Math Kangaroo
Stretch
Arithmetic & Operations
work-backward
The road from Anna's house to Mary's house is 16 km long. The road from Mary's house to John's house is 20 km long. The road from the crossing to Mary's house is 9 km long. How long is the road from Anna's house to John's house?
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Answer: E — 18 km
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Hint 1 of 3
Notice the two roads cross in the middle ā that crossing is on the way from Anna to John.
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Hint 2 of 3
Both long roads (Anna-to-Mary and John-to-Mary) include the same 9 km piece up to Mary.
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Hint 3 of 3
Take that 9 km off each road to find Anna-to-crossing and John-to-crossing, then add them.
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Approach: break each road at the crossing, then add the two near pieces
- Anna's road to Mary is 16 km, but the last 9 km is from the crossing to Mary, so Anna to the crossing is 16 ā 9 = 7 km.
- John's road to Mary is 20 km, and again 9 km of it is from the crossing to Mary, so John to the crossing is 20 ā 9 = 11 km.
- Anna to John goes through the crossing: 7 + 11 = 18 km.
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