Problem 3 · AMC 8 Stretch
Core
Arithmetic & Operations
Logic & Word Problems
logical-reasoningwork-backwardidentifying-relevant-data
Mr. Mayer takes the 7:25 bus to his office in the morning, then walks home in the afternoon. The whole day's travel (bus there + walk back) takes 1 hour 10 minutes. If he walked BOTH ways, it would take 1 hour 50 minutes. How long would it take him to take the bus BOTH ways?
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Answer: 30 minutes by bus both ways
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Hint 1 of 4
Give names to the two one-way times: let \(W\) = time to walk one way, \(B\) = time to bus one way.
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Hint 2 of 4
Walking both ways means \(W + W = 1\) hour 50 minutes. So \(2W = 110\) minutes — find \(W\).
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Hint 3 of 4
Bus-then-walk means \(B + W = 1\) hour 10 minutes = 70 minutes. Once you know \(W\), subtract to get \(B\).
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Approach: Work backward to the one-way times, then double the bus time
- Let \(W\) be the one-way walking time and \(B\) the one-way bus time, in minutes.
- Walking both ways takes 1 h 50 min = 110 min, and that is \(W + W\): \(2W = 110\), so \(W = 55\) min.
- Bus-then-walk takes 1 h 10 min = 70 min, and that is \(B + W\): \(B + 55 = 70\), so \(B = 15\) min.
- Both ways by bus takes \(2B = 2 \times 15 = 30\) minutes. (The 7:25 start time is not needed for this; with it, he would arrive at 7:40.)
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