Bunuel wrote:
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour?
(A) 50
(B) 48
(C) 47
(D) 46
(E) 45
Average speed =
\(\frac{TotalDistance}{TotalTime}\)RT = D
T = D/R
Note: dividing distance in miles by rate in miles per hour yields time in hours.*
Total time = (Leg 1 + Leg 2)
Leg 1
time:
\(\frac{D}{r}=\frac{20mi}{60mph}=\frac{20}{60}hrs=\frac{1}{3}\) hour
Leg 2
time:
\(\frac{D}{r}=\frac{20}{40}=\frac{1}{2}\) hour
Total time:
\(\frac{1}{3}hr +\frac{1}{2}hr=\frac{5}{6}\) hour
Total Distance = (20mi + 20mi) = 40 miles
Ave speed*:
\(\frac{40}{(\frac{5}{6})}=40
*\frac{6}{5}=48\) mph
Answer B
*It works because miles units cancel.
\(\frac{miles}{(\frac{miles}{hour})}=(miles*\frac{hour}{miles})=hours\)
**With units. If you stay with time in hours, then you don't need units, but that fact may not be obvious. This example is \(\frac{D}{t}=r\):
\(\frac{40miles}{(\frac{5}{6}hour)}=(40miles * \frac{6}{5hrs})=48\frac{miles}{hour}=48mph\)
\(\frac{miles}{hour}\) IS mph
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