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Benjamin and Bob are marathon runners on a run from landmarks P to Q. Benjamin runs half the way and walks the other half. Bob runs half the time, and walks the other half. The two run at the same speed and walk at the same speed. Who finishes first?

(b) Which approach was the most (i) effective (ii) appropriate way of starting the problem?

Looks like a tie. What approaches are given to you.

Did you know?

Did you know that when Benjamin and Bob are marathon runners on a run from landmarks P to Q, both running at the same speed and walking at the same speed, Benjamin finishes first? This may seem counterintuitive since Bob spends half of the time running while Benjamin spends half of the distance running. However, Benjamin's approach of running half of the way and walking the other half allows him to cover the distance in less time overall compared to Bob's approach of running half of the time and walking half of the time. When trying to solve this problem, the most (i) effective and (ii) appropriate way to start is by considering the overall time taken by each runner. Instead of focusing solely on the time spent running or the distance covered, analyzing the total time spent by each runner helps us understand the outcome. This approach allows us to determine that Benjamin finishes first despite spending less time running compared to Bob.