A jogger passed me as I was walking down the street yesterday. I wondered whether I could figure out how fast she was running, so I started paying attention to where the jogger was. When she passed a fire hydrant a short distance in front of me, I began to count seconds. It took me 7 seconds to get to the hydrant, but when I reached the hydrant I looked up to see that she was just passing a parking meter. I again counted seconds until I reached the parking meter, and it took me 10 seconds. When I reached the parking meter, she was passing a light pole. It took me 14 seconds to reach the light pole. I knew that I walked two paces in 1 second, and my pace was 1 yard long. Approximately how fast, in miles per hour, was the jogger moving? (Round your answer to the nearest tenth.)

Question
Asked Nov 11, 2019

 A jogger passed me as I was walking down the street yesterday. I wondered whether I could figure out how fast she was running, so I started paying attention to where the jogger was. When she passed a fire hydrant a short distance in front of me, I began to count seconds. It took me 7 seconds to get to the hydrant, but when I reached the hydrant I looked up to see that she was just passing a parking meter. I again counted seconds until I reached the parking meter, and it took me 10 seconds. When I reached the parking meter, she was passing a light pole. It took me 14 seconds to reach the light pole. I knew that I walked two paces in 1 second, and my pace was 1 yard long. Approximately how fast, in miles per hour, was the jogger moving? (Round your answer to the nearest tenth.)

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Expert Answer

Step 1

The observer reached the hydrant in 7 seconds with a speed oftwo paces in 1 second
where 1 pace is 1 yard. Thus, the speed is 2 yd/s
The distance covered by observer to the hydrant becomes 2yd/sx7s 14yd
The distance covered by jogger to the parking meter becomes 2yd /sx10s = 20yd
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The observer reached the hydrant in 7 seconds with a speed oftwo paces in 1 second where 1 pace is 1 yard. Thus, the speed is 2 yd/s The distance covered by observer to the hydrant becomes 2yd/sx7s 14yd The distance covered by jogger to the parking meter becomes 2yd /sx10s = 20yd

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Step 2

...
Thus
14yd
20yd
2yd/s xyd/s
20x2
-2.857
14
That is, the joggers speed is 2.857 yd/s
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Thus 14yd 20yd 2yd/s xyd/s 20x2 -2.857 14 That is, the joggers speed is 2.857 yd/s

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