Upper and Lower Bounds. Help needed.?

Question

Hey. I've got some questions on the topic of Upper and Lower bounds in which i have some difficulties with. All comments will be so much appreciated. Many thanks!

1. A car travels 5000m, correct to the nearest metre, in 2 minutes 21.7 seconds, correct to the nearest tenth of a second. Find the upper and lower bounds of the average speed in metres per second.

Regarding question 2 i found that at the end it requires you to divide certain upper bounds with certain lower bounds. I did convert the 2 minutes into 160 seconds and added it onto the 21.7. I found the upper and lower bounds by using add and sub and using 10 and 1/10 for the secnd. Why do you divide instead of normal multiplying with the bounds? Why do you this to certain bounds? Also has Speed = Distance/Time got something to do with this?

Many thanks! All comments are so very much appreciated.

Answer 1

( 60 x 2 ) + 21.7 = 141.7 seconds as you said.

141.7 upper and lower bounds for time :

U.B. ==> 141.7 + 1/2 x 0.1 = 141.75

L.B. ==> 141.7 - 1/2 x 0.1 = 141.65

[141.65,141.75)

5000m upper and lower bounds for distance :

U.B. ==> 5000 + 1/2 x 1 = 5000.5

L.B. ==> 5000 - 1/2 x 1 = 4999.5

[4999.5,5000.5)

I see what you mean...Here's your explanation for question 2:

Yes, it does have to do with the equation of speed = distance/time

Now we got the U.B. and L.B. of both distance and time, we need to find it for speed.

Now think with me... Since  [ Speed = Distance / Time ]

Think of it this way...you'll get the highest magnitude of speed when you cover the largest distance in the smallest possible time, i.e:

Maximum magnitude of speed = Greatest magnitude of distance/ Least magnitude of time

From this defintion comes finding the U.B., maximum speed ( the U.B. ) we could possibly ever get from the given info is by dividing the U.B. of distance (maximum possible value) with the L.B of time (minimum possible value).

Hence:

Speed U.B. = U.B. Distance/ L.B. Time = 5000.5/141.65 = 35.30180021......m/s

Same applies to the argument of L.B. of speed.

The minimum value that we could ever possibly get goes with the L.B. of distance ( minimum possible value ) with the U.B. of time ( maximum possible value ).

Hence:

Speed L.B. = L.B. Distance/ U.B. Time = 4999.5/141.75 = 35.26984127...m/s

It all depends on the equation you got/ the relation between the variables.

Say you have an equation like .. : Mass= Density x Volume

Then:

Mass U.B. = Density U.B. x Volume U.B.

Mass L.B. = Density L.B. x Volume L.B.

Maximum mass = max density x max volume

You can think of it this way:

A greater product results when you multiply bigger numbers, hence the U.B. of density and volume for finding the U.B. of mass, and vice versa.

Hope this helps.

Notes:

Person above (Hy) didn't convert 2 minutes and 21.7 seconds to seconds only, so answers are wrong but explanation is right.

U.B. = Upper Bound

L.B. = Lower Bound