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qaws [65]
3 years ago
14

The speed limit is 25 miles per hour, but it seems that many of the cars are going faster. The city places 2 counter strips 360

feet apart in the lane closest to the school.A teacher times one car's front tires crossing the strips in the 7.0 sec. Is the car speeding? How do you solve this?
Mathematics
1 answer:
klio [65]3 years ago
7 0
You figure out how long it would take a car traveling at 25 mph
to cover 360 ft.  Any driver who does it in less time is speeding.

           (25 mi/hr) · (5,280 ft/mile) · (1 hr / 3,600 sec)

       =    (25 · 5280 / 3600)  ft/sec  =  (36 and 2/3) feet per second.

To cover 360 ft at 25 mph, it would take

                360 ft / (36 and 2/3 ft/sec)  =   9.82 seconds .

Anybody who covers the 360 feet in less than 9.82 seconds
is moving faster than 25 mph.
_________________________________

If you're interested, here's how to do it in the other direction:

Let's say a car covers the 360 feet in ' S ' seconds.
What's the speed of the car ?

           (360 ft / S sec) · (1 mile / 5280 feet) · (3600 sec/hour)

       =    (360 · 3600) / (S · 5280)  mile/hour

       =        245.5 / S    miles per hour .

The teacher timed one car crossing both strips in 7.0 seconds.
How fast was that car traveling ?

                   245.5 / 7.0  =  35.1 miles per hour


Another teacher timed another car that took 9.82 seconds to cross
both strips.  How fast was this car traveling ?

                        245.5 / 9.82  =  25 miles per hour
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Data given and notation  

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If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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We can replace in formula (1) the info given like this:  

t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50    

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