You are walking around a lake with a circumference of 6 miles. 2/3 of the way ar

Question

You are walking around a lake with a circumference of 6 miles. 2/3 of the way around the lake from where you parked your car, you see a runner approaching you wearing a tee-shirt with writing on it. You can read the first two lines on the shirt, but unable to read the last before he passes you.You are curious of what the last line said. You wonder if you will pass him again before you get back to your car.Your walking speed is 3 miles per hour and the runners speed is 7 miles per hour. Assume the runner runs one more lap, will you have another chance to read the shirt? If so, how long do you have before your second chance and how far away from your car will you be when this happens?

Explanation / Answer

Hi, Given the circumference of the lake = L = 6 miles,             the speed of runner = v2 = 7 miles per hour and             the our speed = v1 = 3 miles per hour. If we are walking in the same direction as the runner is running, there is no way we can cross the runner since his speed is more than ours. Hence we should start walking in the opposite direction to the runner. Now, let us assume the runner is running clockwise and we are walking anti-clockwise direction along the lake circuumference. Let us imagine he crossed us at a time 't'. Then in this time we will cross a distance say s1 and the runner will cross a distance s2. However, since we crossed each other, sum of these should be equal to the circumference of the lake. i.e., s1 + s2 = L => (v1 * t) + (v2 * t) = L   => 3t + 7t = 6 miles. => 10t = 6 miles. => t = 0.6 hours. So we will have a second chance after 0.6 hours = 36 min. And in this time, we would have walked a distance of s1 = 3 * 0.6 = 1.8 miles from the car. And in this time, we would have walked a distance of s1 = 3 * 0.6 = 1.8 miles from the car. Hope this helps you.

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