Question

It’s a sunny Saturday afternoon and you are walking around the lake by your house, enjoying the last few days of summer. The sidewalk surrounding the perimeter of the circular lake is crowded with walkers and runners. You then notice a runner approaching you wearing a T-shirt with writing on it. You read the first two lines, but are unable to read the third line before he passes. You wonder, ”Hmmm, if he continues around the lake, I bet I’ll see him again but I should anticipate the time when we’ll pass again.”
You look at your watch and it is 5:07pm. You estimate your walking speed at 3 m/s and the runner’s speed to be about 14 m/s. You also estimate that the diameter of the lake is about 2
miles. At what time should you expect to read the last line of the t-shirt?

Answer 1

The anticipated time when he will appear again is 5:17 pm

The given parameters;

your speed, $V_a$ = 3 m/s

the runner's speed, $V_b$ = 14 m/s

the diameter of the lake, d = 2 miles = 3218.69 meters

• Let the anticipated time when he will appear again = t

The circumference of the lake is calculated as;

$C = \pi d\\\\C = 3.142 \times 3218.69 = 10,113.12 \ m$

Apply concept of relative velocity to determine the time, in which he will appear again.

By the time he appears again;

the distance you moved + distance he moved = circumference of the circle

$V_at + V_bt = 10, 113.12\\\\(V_a + V_b)t = 10,113.12\\\\(3 + 14) t = 10,113.12\\\\17t = 10,113.12\\\\t = \frac{10,113.12}{17} \\\\t = 594.89 \ s = 9.92 \ \min \ \approx 10 \ \min$

$t\ \approx \ \ 5:17 \ pm$

Thus, the anticipated time when he will appear again is 5:17 pm

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