Question

How often would Jeff have needed to measure Roger's speed in order to find lower and upper estimates within 0.1 mile of the actual distance he ran?

Answer 1

any idea? im totally lost

Answer 2

It's a bit of a tricky question. If we decrease the interval, we'll need new information for those new interval points. We don't have that kind of information.

In such a rough application, it may be common simply to cut the interval in half.

With the interval set at 1/4 hour, the spread is 14 - 11 = 3

¼(11 + 9 + 9 + 8 + 7 + 0) = 11
¼(12 + 11 + 9 + 9 + 8 + 7) = 14

Let's just use the previous value and assume all went well for 15 minutes

(1/8)(12+11+11+9+9+9+9+8+8+7+7+0+0) = 100/8 = 12.5
(1/8)(12+12+11+11+9+9+9+9+8+8+7+7+0) = 14

And we've decreased the spread to 14 - 12.5 = 1.5

Unfortunately, we really don't have that intermediate data. In this form, the upper bound never will change.

(1/16)(12+12+12+4(11+9+9+8+7+0)) = 212/16 = 13.25
Giving 14 - 13.25 = 0.75


(1/32)(12+6(12)+8(11+9+9+8+7+0)) = 436/32 = 13.625
Giving 14 - 13.625 = 0.375

Recap:

1/4 ------ 3 = 3/1
1/8 ------ 1.5 = 3/2
1/16 ----- 0.75 = 3/4
1/32 ----- 0.375 = 3/8

Looks like a predicable pattern!

Answer 3

so would the final answer be 1/64?

Answer 4

1/64?

Is 3/16 < 0.10

Keep in mind that this is just one scheme of how to interpolate the data between where it was actually recorded. It will happen faster or slower with other schemes. This one is particularly unsatisfying because the upper bound won't move.

Answer 5

oh whoops i ment 1/128

Answer 6

There you go.

Answer 7

now what units is that in exact? ...the problem asks for it in minutes