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Time taken downstream

by binaras » Sun Apr 26, 2015 11:41 pm
Hi

in the attacehed question

i used the following formuala set
upstream > 90 = (v-3)(t+0.5)
downstream> 90 = (v+3)t
However with this formula I wasn't able to solve the problem.

When I used the following formuala set I was able to solve the problem.
upstream > 90 = (v-3)t
downstream> 90 = (v+3)(t-0.5)

I would like to understand why the first formula set is wrong.

Thanks, B
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by GMATGuruNY » Mon Apr 27, 2015 3:10 am
A boat traveled upstream a distance of 90 miles at an average speed of
(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
We can PLUG IN THE ANSWERS, which represent the number of hours that the boat took to travel downstream.
The most likely answer choice is A -- the only option that divides evenly into 90.

Answer choice A: 2.5 hours to travel downstream.
Rate downstream = d/t = 90/(2.5) = 36 miles per hour.
Thus, v+3 = 36, implying that v=33.
Rate upstream = v-3 = 33-3 = 30 miles per hour.
Time upstream = d/r = 90/30 = 3 hours.
Time upstream - time downstream = 3-2.5 = .5.
Success!

The correct answer is A.
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by Brent@GMATPrepNow » Mon Apr 27, 2015 8:31 am
A boat travelled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then travelled 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
I like to begin with a "word equation." We can write:
travel time upstream = travel time downstream + 1/2

Time = distance/rate
So, we can replace elements in our word equation to get:
90/(v-3) = 90/(v+3) + 1/2

Now solve for v (lots of work here)
.
.
.
v = 33

So, travel time downstream = 90/(v+3)
= 90/(33+3)
= 90/36
= 5/2
= [spoiler]2 1/2 hours[/spoiler]
= A

ASIDE: Once you create the equation 90/(v-3) = 90/(v+3) + 1/2, you may realize this this will take a while to solve. If your algebra skills are weak/slow, you might consider plugging in the answer choices, as this might be faster.

Cheers,
Brent
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by [email protected] » Mon Apr 27, 2015 10:17 am
Hi binaras,

This is a layered story-problem and takes a lot of effort to solve using a traditional "math approach" (Brent notes in his explanation: "lots of work here"). Here's how you can solve it with a bit of logic and TESTing THE ANSWERS:

From the prompt, we can create 2 equations:

D = R x T

90 = (V-3)(T + 1/2)
90 = (V+3)(T)

We're asked for the value of T.

From the prompt, I find it interesting that the distance is a nice, round number (90).... because when looking at the answer choices, most of them are NOT nice decimals. When multiplying two values together (as we do in BOTH equations), if you end up with a round number, chances are that either....

1) both numbers are round numbers
2) one of the numbers includess a nice fraction (e.g. 1/2) which can be multiplied and the end result will be a round number.

This gets me thinking that 2.5 is probably the answer, but I still have to prove it....I'm going to plug in THAT value for T and see what happens to the 2 equations....

90 = (V-3)(3)
90 = (V+3)(2.5)

30 = (V-3)
36 = (V+3)

33 = V
33 = V

Notice how both values of V are THE SAME? That means that we have the solution. V=33 and T=2.5

Final Answer:A

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