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Tara drove at an average speed of 50 miles per hour for the first 50

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sashiim20
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Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   04 Sep 2017, 23:11
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Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip?

(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
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C
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Bunuel
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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   04 Sep 2017, 23:30
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sashiim20 wrote:
Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip?

(A) 50
(B) 55
(C) 60
(D) 65
(E) 70


(average speed) = (total distance)/(total time) = \(\frac{50 + 50}{\frac{50}{50} + \frac{50}{75}}=\frac{100}{\frac{5}{3}}=60\).

Answer: C.
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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   04 Sep 2017, 23:38
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Bunuel wrote:
sashiim20 wrote:
Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip?

(A) 50
(B) 55
(C) 60
(D) 65
(E) 70


(average speed) = (total distance)/(total time) = \(\frac{50 + 50}{\frac{50}{50} + \frac{50}{75}}=\frac{100}{\frac{5}{3}}=60\).

Answer: C.


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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   06 Sep 2017, 03:37
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sashiim20 wrote:
Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip?

(A) 50
(B) 55
(C) 60
(D) 65
(E) 70


Either use the total distance/ total time concept

or the Average speed eqn =2V1V2/V1+V2.

So 2*50*75/(50+75)= 60
Ans:C
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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   11 Sep 2017, 11:05
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sashiim20 wrote:
Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip?

(A) 50
(B) 55
(C) 60
(D) 65
(E) 70


We can use the following formula:

average speed = (distance 1 + distance 2)/(time 1 + time 2)

We see that time 1 = 1 hour, time 2 = 50/75 = 2/3 hours, and distance 1 = distance 2 = 50 miles. Thus:

average = (50 + 50 )/(1 + 2/3)

average = 100/(5/3) = 300/5 = 60 mph.

Answer: C
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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   08 Sep 2019, 02:17
In such cases just take the harmonic mean (HM).

HM of A and B = 2 (A*B)/(A+B).
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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink] New post   26 Oct 2020, 06:51
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Re: Tara drove at an average speed of 50 miles per hour for the first 50 [#permalink]
26 Oct 2020, 06:51
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