Bunuel wrote:
Sarah goes on a 600-mile trip. She travels at a constant rate of 50 miles per hour for the first 300 miles of the trip, and at a constant rate of 100 miles per hour for the last 300 miles of the trip. What is Sarah’s average speed in miles per hour for the entire trip?
A 200/3
B 70
C 75
D 80
E 85
(1) The trap is Answer C
Common trap and incorrect option C is the average of the averages: \(\frac{50+100}{2}=75\)
Rule: Even if distance is equal,
we cannot average the average speeds.(If TIME is equal, often we can average the average speeds.* That scenario will be rare.)
(2) Average speed is weighted
We need time traveled for each leg because
Average speed = \(\frac{TotalDistance}{TotalTime}\)
Leg 1, time?\(r*t=D\)
\(50*t_1=300\)
\(t_1=6\) hours
Leg 2, time?\(100*t_2=300\)
\(t_2=3\) hours
Total \(D = 600\)
Total \(t = t_1 + t_2 = 9\) hours
Average speed =
\(\frac{TotalDistance}{TotalTime}=\frac{600mi}{9hrs}=\frac{200}{3}\) mph
Answer A
*Example in which we can average the average speeds because time traveled is equal:
Jake drives at 40 mph for 2 hours, and at 60 mph for 2 hours. Average speed?
Leg 1: 40 mph * 2 hrs = 80 miles
Leg 2: 60 mph * 2 hrs = 120 miles
Total D = 200. Total time = 4
Average speed = Total D/total t= 200/4 = 50 mph = (40 + 60)/2 _________________
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