Maths Question

[cazzle]

I'd really appreciate some help with this poser....

I was out walking with my dog at a steady pace of 12 min per km when my dog ran off at a steady pace to a gate I knew to be 625ft ahead and then returned to me. He did this 4 times in all without stopping. He finally returned to me when we were 81ft from the gate. What speed was my dog running at over this period?

Thanks in advance!

[sp1214]

Isn't it time you bought a lead?

[dundurn]

Your dog runs 4 times as fast as you walk so in the terms of the question at 3mins a km

In the first leg you walk 250ft and the dog runs 625 feet there and 375 ft back to you
2nd leg you walk 150 feet and the dog runs 375feet there and 225 feet back
3rd leg you walk 90 feet, the dog 225ft there and 135 back
final leg you walk 54 feet and the dog runs 135 there and 81 back

you walk in total 544ft, the dog runs 2176ft i.e. 4 times as far

There must be a neat way of explaining this in terms of geometric progressions but I haven't got the time, I'm afraid - just put together a quick and dirty spreadsheet that got me close enough to do a bit of trial and error figuring.

[newtron]

Yeah, I did a quick and dirty spread sheet and got approximately 1137.5 ft/min or 20.8 km/hr.

[cazzle]

Thanks Dundurn & Newtron. I had also done a spreasdheet but wondered if there was a more rigorous way of doing it.