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# rate/time/distance problem

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Intern
Joined: 28 Jun 2008
Posts: 45

Kudos [?]: 140 [0], given: 31

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04 Jun 2009, 20:26
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hey guys, was wondering if anyone had a good method for solving this problem:

During a 40 mile trip, Maria traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x milesw per hour for the last 40-y miles of the trip. The time that Maria took to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?

(1) x=40

(2) y=20

Kudos [?]: 140 [0], given: 31

Current Student
Joined: 03 Aug 2006
Posts: 115

Kudos [?]: 315 [0], given: 3

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09 Jun 2009, 14:12
The best way to solve a DS problem is to reduce it to the lowest form possible.

Lets see what is given in the question.

Actual Scenario (1):
Maria traveled at an average speed of x miles per hour for the first y miles of the trip...
r(ate) x t(ime) = d(istance)

Given r = x miles/hr, d = y miles
=> t1 = y/x

..and at an average speed of 1.25x miles per hour for the last 40-y miles of the trip.

Given r = 1.25x miles per hour, d = 40-y miles
=> t2 = (40-y)/1.25x

so total time t = t1 + t2
$$t = \frac{y}{x} + \frac{40-y}{1.25x}$$

Hypothetical Scenario (2):
The time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip

Given r = x miles per hour, d = 40 miles
=> $$t=\frac{d}{r} = \frac{40}{x}$$

The question is asking $$\frac{time \text{ for scenario 2}}{time \text{ for scenario 1}} \times 100$$

=> $$\frac{\frac{40}{x}}{\frac{y}{x} + \frac{40-y}{1.25x}}\times 100$$

=> $$\frac{\frac{40}{x}}{\frac{1.25y}{1.25x} + \frac{40-y}{1.25x}}\times 100$$

=> $$\frac{\frac{40}{x}}{\frac{1.25y+40-y}{1.25x}}\times 100$$

Solving this further gives us
$$\frac{40\times 1.25}{40+0.25y} \times 100$$

So basically the question is asking $$y=?$$

Looking at the statements the only statement that provides this information is statement 2.

Kudos [?]: 315 [0], given: 3

Re: rate/time/distance problem   [#permalink] 09 Jun 2009, 14:12
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