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rate/time/distance problem

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Intern
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Joined: 28 Jun 2008
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rate/time/distance problem [#permalink]

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New post 09 Jun 2009, 19:51
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Gi guys was wondering if anyone had a good method to solve this problem:

On his trip from Alba to Benton, Julio drove the first X miles at an average speed of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first X miles?

(1) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
(2) On this trip, it took Julio four more hours to drive the first X miles than to drive the remaining distance.

Answer: A.
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Schools: Haas School of Business
Re: rate/time/distance problem [#permalink]

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New post 09 Jun 2009, 22:55
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Lets assume the total distance traveled is \(d\)

\(rate \times time = distance\)

For the 1st segment
\(rate = 50\)

\(distance = x\)

\(time = \frac{x}{50}\)

For the second segment
\(rate = 60\)

\(distance = d - x\)

\(time = \frac{d-x}{60}\)

The question is asking us for the value of x.

Total time for both segments
\(t=\frac{x}{50}+\frac{d-x}{60}\)

which can be simplified to
\(x=300t-5d\)

so basically the question is asking us what is t and what is d.

Lets look at the statements.

Statement 1 gives us what we are looking for:
\(t=10 \text{ and }d=530\)
Hence sufficient.

Now look at the second statement..it tells us segment 1 took four more hours to drive than segment 2.
which is
\(\frac{x}{50}-\frac{d-x}{60}=4\)
however it still does not tell us anything about \(d\)
Hence Insufficient

The answer is A.
Manager
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Location: India
Re: rate/time/distance problem [#permalink]

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New post 10 Jun 2009, 17:01
A.

First lets analyse stmt. 2. It does not talk about distance or time. Hence insuff.

Stmt. 1
Its good to create a diagram for such questions. But i dont know how to draw a diagram on computer and post it. SO i will try to explain it to the best of my capacity.

Journey id in two parts.
Part 1
Av. Speed = 50
Lets time take = T1
Distance covered = D1
Part 2
Av. speed = 60
Time taken = T2
Distance covered = D2

Now - as per stmat 1
T1 + T2 = 10
D1 + D2 = 530
In order to snswer we want D1.
Replace T1,T2 in terms of D1,D2 and we can easily calculate D1.
Re: rate/time/distance problem   [#permalink] 10 Jun 2009, 17:01
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