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# Solution

Irun three times as fast as I walk, and I had walked twice the time I had run. It took me 21 minutes to reach home from the shop. So, suppose I had run for "t" minutes, then I had walked for "2t" minutes. So, t + 2t = 21, or 3t = 21. Thus, t = 7. So, I had walked for 14 minutes and run for 7 minutes.

Let my walking speed be "s", then my running speed is "3s". Suppose I had walked a distance "x" and run a distance "y", then the distance from the shop to my home is d = x + y. Now, distance = speed x time, so x = s x 14, and y = 3s x 7. Therefore d = 14s + 21s = 35s.

If I had run twice as long as I walked, then I would have walked for "t" minutes, and run for "2t" minutes. So, in this case I would have walked a distance of s x t = st, and run a distance of 3s x 2t = 6st. Therefore, total distance is st + 6st = 7st. But, total distance = 35s. Therefore, 7st = 35s, or 7t = 35. Thus, t = 5. Therefore, in this case, I would have walked for 5 minutes and run for "2t" minutes = 2 x 5 = 10 minutes. Thus, it would have taken me 5 + 10 = 15 minutes to reach home from the shop. Did I get that right or, like always, did I bungle it?

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