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A car completed its first 30 miles of a 60-mile trip at an average spe

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A car completed its first 30 miles of a 60-mile trip at an average spe  [#permalink]

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New post 26 Sep 2018, 04:06
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (02:12) correct 30% (02:07) wrong based on 79 sessions

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A car completed its first 30 miles of a 60-mile trip at an average speed of 60 miles per hour. At what approximate average speed, in miles per hour, did the car complete the remaining miles to achieve an average speed of 50 miles per hour for the entire 60-mile trip? The car completed its 60-mile trip without a break.

(A) 33
(B) 38
(C) 40
(D) 43
(E) 46

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Re: A car completed its first 30 miles of a 60-mile trip at an average spe  [#permalink]

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New post 28 Sep 2018, 13:12
Given 2 equal distances

We can use the shortcut formula

Avg speed = (2*v1*v2)/(v1+v2)

50 = (2*60*v2)/(60+v2)

3,000 + 50v2 = 120v2

3,000 = 70v2

v2 = 3000/70 = 42.8 approximately 43.

Answer choice D

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Re: A car completed its first 30 miles of a 60-mile trip at an average spe  [#permalink]

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New post 12 Oct 2018, 18:18
Salsanousi wrote:
Given 2 equal distances

We can use the shortcut formula

Avg speed = (2*v1*v2)/(v1+v2)

50 = (2*60*v2)/(60+v2)

3,000 + 50v2 = 120v2

3,000 = 70v2

v2 = 3000/70 = 42.8 approximately 43.

Answer choice D

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Hi, can you please help me understand the formula, please? This formula is great, but I don't really understand the rationale. Thanks in advance!
Director
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Joined: 19 Oct 2013
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WE: Engineering (Real Estate)
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A car completed its first 30 miles of a 60-mile trip at an average spe  [#permalink]

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New post 12 Oct 2018, 23:55
1
Gegeyan

Avg speed = total distance/total time

D = V * T

D1 = V1 * T1

D1 = D2 because of the same distance.

D1 = D2 = V2 * T2

T1 = D1/V1

We know that D1 = D2 because it is a total of 60 miles trip and 30 was already completed. This leaves us with another 30 miles.

The equation becomes

avg speed = D1 + D1= 2D1/(D1/V1 + D1/V2)

This then becomes

2D1/ ((V1*D1 + D1*V2)/(V1*V2)

2D1 * (V1*V2)/(D1(V1+V2)

The D1 cancels and becomes 2*V1*V2/(V1+V2)

I hope it is clear now. Let me know if it helps!

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Re: A car completed its first 30 miles of a 60-mile trip at an average spe  [#permalink]

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New post 13 Oct 2018, 00:04
Salsanousi wrote:
Gegeyan

Avg speed = total distance/total time

D = V * T

D1 = V1 * T1

D1 = D2 because of the same distance.

D1 = D2 = V2 * T2

T1 = D1/V1

We know that D1 = D2 because it is a total of 60 miles trip and 30 was already completed. This leaves us with another 30 miles.

The equation becomes

avg speed = D1 + D1= 2D1/(D1/V1 + D1/V2)

This then becomes

2D1/ ((V1*D1 + D1*V2)/(V1*V2)

2D1 * (V1*V2)/(D1(V1+V2)

The D1 cancels and becomes 2*V1*V2/(V1+V2)

I hope it is clear now. Let me know if it helps!

Posted from my mobile device



Thank you so much! Your explanation is clear and helpful! :thumbup: :thumbup: :thumbup: :thumbup: :thumbup: :thumbup: :thumbup:
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Re: A car completed its first 30 miles of a 60-mile trip at an average spe &nbs [#permalink] 13 Oct 2018, 00:04
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A car completed its first 30 miles of a 60-mile trip at an average spe

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