Problem Solving

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

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

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.

Answer choice: dr/(rt-d)
dr/(rt-d) = (12*2)/(2*10 - 12) = 24/8 = 3.

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