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# Sarah goes on a 600-mile trip. She travels at a constant rate of 50 mi

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Sarah goes on a 600-mile trip. She travels at a constant rate of 50 mi  [#permalink]

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21 Jan 2019, 00:06
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Difficulty:

5% (low)

Question Stats:

89% (01:15) correct 11% (01:49) wrong based on 71 sessions

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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

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Re: Sarah goes on a 600-mile trip. She travels at a constant rate of 50 mi  [#permalink]

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21 Jan 2019, 00:12
Average speed = Total distance/time taken

Average speed = 600/(300/50+300/100) = 600/9 = 200/3

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Sarah goes on a 600-mile trip. She travels at a constant rate of 50 mi  [#permalink]

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23 Jan 2019, 13:57
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

*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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Re: Sarah goes on a 600-mile trip. She travels at a constant rate of 50 mi  [#permalink]

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27 Jan 2019, 19:31
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

We can use the formula: average rate = total distance/total time, and we have:

600/(300/50 + 300/100) = 600/(6 + 3) = 600/9 = 200/3

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Re: Sarah goes on a 600-mile trip. She travels at a constant rate of 50 mi   [#permalink] 27 Jan 2019, 19:31
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