# Upper lower bound question

1. Apr 10, 2007

### thomas49th

1. The problem statement, all variables and given/known data
Martin won the 400 metre race in a time of 1 minute
The time was correct to a tenth of a second
The distance was correct to 1cm

Find the upper and lower bounds of Martin's speed in km/h

2. Relevant equations
Speed = distance over time

3. The attempt at a solution
400 = 0.4km to 1 cm it's 0.4005 or 0.3995
1 second = 0.00277777777777 hours

how do I find the upper and lower bounds for a tenth of a second from the number above (it's recurring).

THe upper bound of speed = upper bound of distance/lower bound of time
The lower bound of speed = lower bound of distance/upper bound of time

Thanks

2. Apr 10, 2007

### HallsofIvy

Staff Emeritus
You've misplaced a decimal position. If the distance is "correct to the nearest cm"- i.e. rounded to the nearest centimeter, then it could be as much as 400 m+ .5 cm= 400 m+ .005 m= 400005 m = .400005 km. Similarly, if could be as low as 400m- .005 m= 399.995 m= .499995 km.

For the "nearest tenth of a second", the true time could be as low as 1 min+ .5 second= 1 min+ .008333 min= 1.008333 min= 0.0168055 hr or as low as 1 min- .5 second= 1 min- .008333 min= .99166 min= .016528 hr.

You don't need to get an exact value do you?
"The upper bound of speed = upper bound of distance/lower bound of time"
so .400005 km/.016528 hr= 24.20 km/hr
"The lower bound of speed = lower bound of distance/upper bound of time"
so .499995 km/0.0168055 hr = 29.75 km/hr.

If you do need the exact value then leave the numbers in fraction form.
The maximum distance is 400.005 m= 0.400005= 400005/1000000 km and the minimum distance is .49995= 499995/1000000 km.
The minimum time is 1- (1/2)/60= 1- 1/120= 119/120 min= 119/7200 hr and the maximum time is 1+ (1/2)/60= 1+ 1/120= 121/120 minutes= 121/7200 hr.

The upper bound on speed is (400005/1000000)(7200/119)= 2880036/11900000 km/hr while the lower bound on speed is (499995/1000000)(7200/121)= 3599964/12100000 km/hr. Those, of course, can be reduced.

3. Apr 10, 2007

### thomas49th

The actual question is:

4. Apr 11, 2007

### thomas49th

Code (Text):
You don't need to get an exact value do you?
"The upper bound of speed = upper bound of distance/lower bound of time"
so .400005 km/.016528 hr= 24.20 km/hr
"The lower bound of speed = lower bound of distance/upper bound of time"
so [COLOR="Red"].499995 [/COLOR]km/0.0168055 hr = 29.75 km/hr.
isn't it .399995 = 23.801km/h

and isn't the upper bound

.400005 / 0.016805555 = 23.802km/h