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Car X traveled from city A to city B in 30 minutes. The first half of

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Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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New post 16 Nov 2019, 15:07
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A
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E

Difficulty:

  35% (medium)

Question Stats:

78% (01:58) correct 22% (02:23) wrong based on 59 sessions

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Car X traveled from city A to city B in 30 minutes. The first half of the distance was covered at 50 miles per hour, and the second half of the distance was covered at 60 miles per hour. What was the average speed of car X?

A. 200/11
B. 400/11
C. 500/11
D. 600/11
E. 700/11
Spoiler: OA

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Re: Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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New post 16 Nov 2019, 18:39
Bunuel wrote:
Car X traveled from city A to city B in 30 minutes. The first half of the distance was covered at 50 miles per hour, and the second half of the distance was covered at 60 miles per hour. What was the average speed of car X?

A. 200/11
B. 400/11
C. 500/11
D. 600/11
E. 700/11



Here equal distance is covered in two different speeds, so the overall average =2ab/(a+b)=2*50*60/(50+60)=6000/110=600/11

D
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Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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New post Updated on: 01 Dec 2019, 05:06
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\(Ave.Speed= \frac{Distance}{ (t1+ t2)}\)

\(—> \frac{D}{2}= 50* t1–> t1= \frac{D}{100}\)

—> \(\frac{D}{2}= 60* t2–> t2= \frac{D}{120}\)

\(Ave.speed= \frac{D}{(D/100 + D/120)}= \frac{D}{(11D/600)}= \frac{600}{11} \)

The answer is D

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Originally posted by lacktutor on 17 Nov 2019, 02:29.
Last edited by lacktutor on 01 Dec 2019, 05:06, edited 3 times in total.
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Re: Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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New post 18 Nov 2019, 21:11
Bunuel wrote:
Car X traveled from city A to city B in 30 minutes. The first half of the distance was covered at 50 miles per hour, and the second half of the distance was covered at 60 miles per hour. What was the average speed of car X?

A. 200/11
B. 400/11
C. 500/11
D. 600/11
E. 700/11


Answer is D

Explanation: total Distance (d) = d1 + d2 = 50 mph * t1 + 60mph * t2;
We are also told that d1 = d2;
So: 50 t1 = 60t2;

t = 30 minutes = 0.5 hour;
t1 + t2 = 0.5 hour;
So: t1 = 0.5 - t2;

Solve 2 equations, 2 unknowns:
(1) 50t1 = 60t2 and (2) t1 = 0.5 - t2

t2 = 25/110

t1 = 0.5 - t2 = 55/110 - 25/110 = 30 /110 = 3/11;

Ave speed = d / t = (50t1 + 60t2) / 0.5
= (50 * 3/11 + 60*25/110 ) /0.5
= (150/11 + 150/11) / 0.5
= (300/11)/ 0.5
= 600/11


Please give kudos if you find my Explanation, Really need it :thumbup: :thumbup:
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Re: Car X traveled from city A to city B in 30 minutes. The first half of   [#permalink] 18 Nov 2019, 21:11
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