Guide 3: Chapter 12; Pg. 187; Problem 5

[lionelpq]

A cyclist traves the length of a bike path that is 225m long, rounded to the nearest mile. IF the trip took him 5h rounded to the nearest h, then his average speed must be between:

-Why is the answer 40 to 51. If the max speed is 50+1/9 and min is 40+9/11, shouldnt average speed be between 41 and 50 (i.e why is this rounded differently)?

Thanks

[jnelson0612]

Hi lionel,
I think the part to focus on is what the the words "must be between" mean. If I know that my range of possible values is 40 9/11 to 50 1/9, including those values, then it does make sense that the average speed is between 40 and 51. If I try to say that it is between 41 and 50, then I am leaving out every value below 41 and every value above 50. We know that we have many such values that work: everything from 40 9/11 to 41, and everything from 50 to 50 1/9.

Thank you,

[sonitushar]

Please correct me if I am wrong. Since miles and hours are rounded, I believe the miles should be between 224.5 and 225.4. Similarly the hours should be between 4.5 and 5.4. Because if the miles are 225.5 and hours as 5.5 then they will be rounded to 226 and and 6 respectively. I solved using these boundaries and I get the answer of between 41 and 51. Therefor (E).

Could you clarify this?

Thank you!

[tim]

225.4 is definitely not an acceptable upper bound, because that precludes 225.45 from being an option. in reality, 225.49 and 225.49999999999 work, so 225.5 is the upper bound. note that the problem uses the word "between", so that means the boundary points are excluded anyway, so using 225.5 basically just means that the length is less than 225.5, which is true given the fact that it rounds to 225..