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# Aaron traveled from New York to New Jersey in 45 mins. What

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SVP
Joined: 21 Jul 2006
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Aaron traveled from New York to New Jersey in 45 mins. What [#permalink]  19 Nov 2007, 13:37
Aaron traveled from New York to New Jersey in 45 mins. What was Aoron's average speed?

(1) Aaron traveled 68.9 kilometers on this trip. (1 kilometer = 0.6214 miles)

(2) One-third the distance of the trip was traveled at 50 miles per hour, and the other two thirds of the distance was traveled at 60 miles per hour.

This is an easy question. OA is D. However, i'm not too sure how to set up the equation for statement 2. I know that I can reach to an answer with this information, but i'm just not sure how to create an equation. Would someone please show me how? thank you
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2143 [0], given: 359

Expert's post
2)

NY-------0---------------NJ

S- total distance
V1,V2 - speed
Va-average speed
S1,S2 - distance (S1=(NY,0), S2=(0,NJ)
t - time

one knows:
t
S=S1+S2
n=S1/S
m=S2/S
------------------------

t=t1+t2=(S1/V1+S2/V2)
Va=S/t=S/(S1/V1+S2/V2)=(1/(n/V1+m/V2))=V1*V2/(n*V2+m*V1)

Va=50*60/(60/3+50*2/3)=50*60*3/160~56.3 (miles/h)
SVP
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according to the explanation, this is how they did:

50(1/3) + 60(2/3) = 56 2/3

But honestly, I don't see the logic of this approach. Now imagine you have this problem instead:

Tom drove from his house to school at a spead of 30 mph. Tom then drove through the same road back home at a speed of 40 mph. What was Tom's average speed?

now, if i apply the same logic from the first example to the second one, you wouldn't get the right answer cause you would get:

30(1) + 40(1) = 70 which is wrong

so what makes these 2 problems different?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2143 [0], given: 359

Expert's post
the same logic:

S/V1+S/V2=2S/Va

Va=2*(1/V1+1/V2)

Va=2*30*40/(30+40)=34 2/7
SVP
Joined: 21 Jul 2006
Posts: 1551
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Kudos [?]: 305 [0], given: 1

thanks! appreciate it
CEO
Joined: 29 Mar 2007
Posts: 2591
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Re: Average Speed [#permalink]  21 Nov 2007, 10:20
tarek99 wrote:
Aaron traveled from New York to New Jersey in 45 mins. What was Aoron's average speed?

(1) Aaron traveled 68.9 kilometers on this trip. (1 kilometer = 0.6214 miles)

(2) One-third the distance of the trip was traveled at 50 miles per hour, and the other two thirds of the distance was traveled at 60 miles per hour.

This is an easy question. OA is D. However, i'm not too sure how to set up the equation for statement 2. I know that I can reach to an answer with this information, but i'm just not sure how to create an equation. Would someone please show me how? thank you

1) suff.

2) 50t=X/3 60T=2X/3

t+T=45min or 45/60 9/12--> 3/4hr

(X/3)/50+(2X/3)/60=3/4hr

Were looking for Total time/ Total Distance, we have the time, we need distance, which is X.

X/150+2X/180=3/4 --> X/150+X/90 --> 3X/450+5X/450=3/4

8X=450(3/4) --> 8X=337.5 --> X~42miles.

So 42miles/3/4hr---> 168/3 =56mph answer is aprox. 56mph.
Senior Manager
Joined: 06 Aug 2007
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Re: Average Speed [#permalink]  23 Nov 2007, 22:58
GMATBLACKBELT wrote:
tarek99 wrote:
Aaron traveled from New York to New Jersey in 45 mins. What was Aoron's average speed?

(1) Aaron traveled 68.9 kilometers on this trip. (1 kilometer = 0.6214 miles)

(2) One-third the distance of the trip was traveled at 50 miles per hour, and the other two thirds of the distance was traveled at 60 miles per hour.

This is an easy question. OA is D. However, i'm not too sure how to set up the equation for statement 2. I know that I can reach to an answer with this information, but i'm just not sure how to create an equation. Would someone please show me how? thank you

1) suff.

2) 50t=X/3 60T=2X/3

t+T=45min or 45/60 9/12--> 3/4hr

(X/3)/50+(2X/3)/60=3/4hr

Were looking for Total time/ Total Distance, we have the time, we need distance, which is X.

X/150+2X/180=3/4 --> X/150+X/90 --> 3X/450+5X/450=3/4

8X=450(3/4) --> 8X=337.5 --> X~42miles.

So 42miles/3/4hr---> 168/3 =56mph answer is aprox. 56mph.

Re: Average Speed   [#permalink] 23 Nov 2007, 22:58
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