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rate/time/distance problem

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Intern
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rate/time/distance problem [#permalink]

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New post 04 Jun 2009, 21:20
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Hi guys, was wondering if anyone could offer a good explanation on how to solve this problem:

A boat traveled upstream a distance of 90 miles at an average speed (v-3) miles per hour and then traveled the same distance downstream at an average speed of (v+3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1

Answer: A.

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Manager
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Location: India
Re: rate/time/distance problem [#permalink]

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New post 05 Jun 2009, 02:25
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Here are the steps.

In question we have 2 unknown variables. V in rate and time T. But if looked carefully it says the differance in average speed between upstream and downstream is 6.

I choose downstream speed as x miles/hour
Now upstream speed is x-6 miles/hour

For downstream, use Rate x Time = Distance which is x*t = 90 => x = 90/t ------------(I)

Now for upstream, (x-6)*(t+1/2) = 90 -----------------(II)

Use value of x from (I) in (II)

(90/t-6)*(t+1/2) = 90

6t^2 + 3t - 45 = 0
On solving this gives

t = 2.5 and -3. Time can't be in -ve so 2.5 is the answer.

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Senior Manager
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Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Re: rate/time/distance problem [#permalink]

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New post 05 Jun 2009, 02:26
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U D
R (v-3) (v+3)
T t+30 t
D 90 90


(v-3)(t+0.5)=(v+3)t
vt+0.5v-3t-1.5=vt+3t
0.5v-3t-1.5=3t
v/2-6t=3/2
v=3+12t

using downstream eqn.
(3+12t+3)t=90
6t+12t^2-90=0
?????
what nextt.....
OA / explanation plase
_________________

Lahoosaher

Kudos [?]: 228 [1], given: 16

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Senior Manager
Senior Manager
User avatar
Joined: 16 Jan 2009
Posts: 356

Kudos [?]: 228 [1], given: 16

Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Re: rate/time/distance problem [#permalink]

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New post 05 Jun 2009, 02:43
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Hey humans,

Thanks for the explanation .....I missed the difference in the avg speed.
_________________

Lahoosaher

Kudos [?]: 228 [1], given: 16

Re: rate/time/distance problem   [#permalink] 05 Jun 2009, 02:43
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