Question 566810
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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