## Rate, distance and time problem

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### Rate, distance and time problem

by gmattesttaker2 » Thu Sep 13, 2012 8:05 pm
Hello,

This is from MGMAT Guide 3. P. 110. Can you please assist here? Thanks a lot.

A park ranger travels from his base to a campsite via truck at r miles per hour. Upon arriving, he collects a snowmobile and uses it to return to base. If the campsite is d miles from the park ranger's base and the entire trip took t hours to complete, what was his speed on the snowmobile, in terms of t, d, and r ?

Ans: [spoiler]dr/(rt-d)[/spoiler]

My approach was as follows:

Rate x Time = Distance
------------------------
r x t1 = d
? x t2 = d

Since entire trip took t hours to complete, (r + ?) x (t1 + t2) = 2d
So, (r + ?) x t = 2d

So, r + ? = 2d/t

However, I am not sure if this approach is correct. Can you please assist? Thanks a lot for your help - Sri

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by das.ashmita » Thu Sep 13, 2012 8:44 pm
My approach was as follows:

Rate x Time = Distance
------------------------
r x t1 = d
? x t2 = d
Hi Sri
Your approach till the step above is correct.
However, after this you have to take one speed at a time.

t1 = d/r
t2 = d/x

t = t1 + t2
=>t = d/r+d/x
=>x = dr/(tr-d)

Hope it helps

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by Brent@GMATPrepNow » Fri Sep 14, 2012 7:03 am
gmattesttaker2 wrote: A park ranger travels from his base to a campsite via truck at r miles per hour. Upon arriving, he collects a snowmobile and uses it to return to base. If the campsite is d miles from the park ranger's base and the entire trip took t hours to complete, what was his speed on the snowmobile, in terms of t, d, and r ?
I like to begin these kinds of questions by writing a "word equation"

We're told that the entire trip took t hours to complete, so we can write:
(time in truck) + (time on snowmobile) = t

Let x = the speed of the snowmobile

Note: time = distance/speed

So, time in truck = d/r
And time on snowmobile = d/x

Now take the word equation and replace each part to get:
d/r + d/x = t

Now solve for x. There are several ways to do this. Here's one way.
Multiply both sides by rx (this will eliminate the fractions) to get: dx + dr = trx
Rewrite to get: dr = trx - dx
Factor left side to get: dr = x(tr - d)
Divide both sides by (tr - d) to get: [spoiler]dr/(tr - d)[/spoiler] = x

Cheers,
Brent
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by GMATGuruNY » Fri Sep 14, 2012 7:56 am
gmattesttaker2 wrote:Hello,

This is from MGMAT Guide 3. P. 110. Can you please assist here? Thanks a lot.

A park ranger travels from his base to a campsite via truck at r miles per hour. Upon arriving, he collects a snowmobile and uses it to return to base. If the campsite is d miles from the park ranger's base and the entire trip took t hours to complete, what was his speed on the snowmobile, in terms of t, d, and r ?

Ans: [spoiler]dr/(rt-d)[/spoiler]
Since an actual GMAT problem would offer answer choices, we can plug in values.

Let d = 12 miles and r = 2 miles per hour.
Let the snowmobile rate = 3 miles per hour.
t = time on the truck + time on the snowmobile = 12/2 + 12/3 = 10 hours.
The question asks for the snowmobile rate (3). This is our target.
Now we plug d=12, r=2, and t=10 into the answers to see which yields our target of 3.

dr/(rt-d) = (12*2)/(2*10 - 12) = 24/8 = 3.
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by mohan514 » Sat Sep 15, 2012 5:02 am
i think this problem can be more easily solved by starting from the answer choices

just picking the numbers and then testing the formulae in the answer choices to get the appropriate one

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by Brent@GMATPrepNow » Sat Sep 15, 2012 7:25 am
mohan514 wrote:i think this problem can be more easily solved by starting from the answer choices

just picking the numbers and then testing the formulae in the answer choices to get the appropriate one
Quite possibly. However, plugging in numbers can sometimes take a lot of time.
All student should know both strategies (algebraic and plugging in numbers) for solving this question type (Variables in the Answer Choices).

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