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

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Math Expert
Joined: 02 Sep 2009
Posts: 61484
Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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16 Nov 2019, 14:07
00:00

Difficulty:

35% (medium)

Question Stats:

78% (02:00) correct 22% (02:19) wrong based on 65 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

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Math Expert
Joined: 02 Aug 2009
Posts: 8256
Re: Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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16 Nov 2019, 17:39
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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Joined: 25 Jul 2018
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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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Updated on: 01 Dec 2019, 04:06
2
$$Ave.Speed= \frac{Distance}{ (t1+ t2)}$$

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

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

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

Posted from my mobile device

Originally posted by lacktutor on 17 Nov 2019, 01:29.
Last edited by lacktutor on 01 Dec 2019, 04:06, edited 3 times in total.
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Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: Car X traveled from city A to city B in 30 minutes. The first half of  [#permalink]

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18 Nov 2019, 20:11
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

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
Re: Car X traveled from city A to city B in 30 minutes. The first half of   [#permalink] 18 Nov 2019, 20:11
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