SOLUTION: A motorist goes for a drive, keeping the reading on the speedometer at a constant value of
40 km h
−1
. The speedometer is assumed to be accurate to ± 2 km h
−1
. At the
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40 km h
−1
. The speedometer is assumed to be accurate to ± 2 km h
−1
. At the
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Question 1194498: A motorist goes for a drive, keeping the reading on the speedometer at a constant value of
40 km h
−1
. The speedometer is assumed to be accurate to ± 2 km h
−1
. At the end of the day
he wants to know how far he has travelled, but unfortunately, he forgot to look at the distance
indicator when he set out. He thinks that he drove for four hours, give or take a quarter of an
hour. Estimate how far he travelled and assign an error to your result. Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!
It seems like you are trying to write
It probably makes more intuitive sense to write it as 40 km/hr or 40 km per hour.
The driver sees 40 km/hr, but the speedometer has an error of ± 2 km per hour.
which is the same as writing "an error of plus/minus 2 km per hour"
What this means is that the slowest speed possible is 40-2 = 38 km per hour; while the fastest is 40+2 = 42 km per hour.
In short, the range of possible speeds is between 38 and 42 km per hour, inclusive of both endpoints.
The driver also isn't sure how long he drove. He thinks he drove for 4 hours, give or take 1/4 = 0.25 of an hour.
So the shortest amount of driving time is 4 - 0.25 = 3.75 hours.
The longest possible driving time is 4+0.25 = 4.25 hours.
Let's say the driver is going at the slowest speed in that interval (38 km per hour). Let's also say that they drove for the shortest amount of time (3.75 hours)
Distance = rate*time
Distance = 38*3.75
Distance = 142.5 km
Repeat this for the other possible scenarios.
Making a two-way table helps organize all four possibilities, but it is of course optional.
Shortest Time (3.75 hrs)
Longest Time (4.25 hrs)
Slowest Speed (38 km/hr)
38*3.75=142.5
38*4.25=161.5
Fastest Speed (42 km/hr)
42*3.75=157.5
42*4.25=178.5
The shortest distance traveled is 142.5 km
The longest distance traveled is 178.5 km
Compute the midpoint of those endpoints
(a+b)/2 = (142.5+178.5)/2 = 160.5
We estimate that the driver traveled about 160.5 km
The error is the difference of the midpoint and either extreme
178.5 - 160.5 = 18
160.5 - 142.5 = 18
The error is plus/minus 18 km.
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