Question 566810: A driver averaged 30 mph on a 150-mile trip and then returned over the same 150 miles at the rate of 50 mph. He figured that his average speed was 40 mph for the entire trip.
A. What was his total distance traveled?
B. What was his total time spent for the trip?
c. What was his average speed for the trip?
D. Explain the error in the driver reasoning?
please show work if possible
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! d = rt
150 = 30t
150/30 = t
5 = t
t = 5
So he spent 5 hrs on the first part of the trip
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d = rt
150 = 50t
150/50 = t
3 = t
t = 3
So he spent 3 hrs on the second part of the trip
So in total, he spent 5+3 = 8 hours driving.
The total distance he covered was 150+150 = 300 miles.
So using d = rt again, we can say that d = 300 and t = 8 and use this to find r
d = rt
300 = r(8)
300 = 8r
300/8 = r
37.5 = r
r = 37.5
So the average speed is really 37.5 miles per hour
The error occurs when the driver assumes that speeds can be averaged by simply adding them and dividing them by 2. However, he cannot do this because the faster speed yields more distance traveled, which means that more weight is applied to this speed. This means that a simple average cannot be done (and will not make sense)
If we wanted to use a direct formula, we would have to turn to the formula shown below
Average Speed = (d1+d2)/(d1/r1 + d2/r2)
which is a bit more complicated
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