A boat traveled upstream 90 miles at an average speed of

Question

A boat traveled upstream 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 a half hour longer than the trip downstream, then 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

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1

SeregaP · Answer

first approaching this problem I wrote down what the answer requires: 90/(v+3) or time spent going downstream
from the data let's make up an equation:
90/(v-3)-90/(v+3)=1/2
we can arrive to v^2=1089
v=33
Then be careful!
90/(33+3)=90/36=2,5
Answer is A

EMPOWERgmatRichC · Answer

Hi All,

This is a layered story-problem and takes a lot of effort to solve using a traditional "math approach". 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

GMAT assassins aren't born, they're made, 
Rich

GMATinsight · Answer

Let's try this way

B = Speed of Boat
S = Speed of Stream

Upstream Speed = Net speed against the flow of current = B - S
Downstream Speed = Net speed with the flow of current = B + S

Time upstream = (1/2)Hour + Downstream Time

\frac{90}{v-3} = (\frac{1}{2}) + \frac{90}{v+3}

90/30 = 3
90/36 = 2.5
Diffference = 1/2

i.e. v-3 = 30 and v+3 = 36 i.e. v = 33

Downstream time = 90/36 = 2.5

Answer: Option A

SohamS · Answer

how am i getting this wrong?
time = t for downstream and 1.5t for upstream
Distance upstream = distance downstream (90miles = 90miles)
therefore,
(v-3) 1.5t = (v+3)t
1.5vt-4.5t = vt + 3t
therefore, v = 15mph
Downstream speed = v+3 = 15+3 = 18mph
therefore, time t= d/s = 90/18 = 5hrs

BrentGMATPrepNow · Answer

The question says   "the trip upstream took  a half hour longer  than the trip downstream"  
So, if t = the travel time downstream (in hours), then t + 0.5 = the travel time upstream (in hours)

I have a feeling that you accidentally wrote: t + 0.5  t   = the travel time upstream (which simplifies to be 1.5t)

GMATGuruNY · Answer

We can PLUG IN THE ANSWERS, which represent the number of hours to travel downstream.
The time upstream is 0.5 hour longer than the time downstream.
The correct answer choice is almost CERTAIN to be A -- the only option that implies two times that divide evenly into 90 (2.5 hours and 3 hours).
When the correct answer is plugged in, the difference between the rate downstream (v+3) and the rate downstream (v-3) will be 6 mph:
(v+3) - (v-3) = 6

Answer choice A: 2.5 hours to travel downstream, implying 3 hours to travel upstream 
Rate downstream  = \frac{distance}{time} = \frac{90}{2.5} = 36  mph
Rate upstream  = \frac{distance}{time}= \frac{90}{3} = 30  mph
Rate difference  = 36-30 = 6  mph
Success!

A

kajaldaryani46 · Answer

—-

Hi  Bunuel ,

Thanks for explaining this so well. Could u pls post a list of similar boat stream Qs

Posted from my mobile device

Bunuel · Answer

GRS · Answer

Dear experts, can you help me in this approach. I am getting it wrong.

(i) Upstream
 v-3 = \frac{90}{t+\frac{1}{2}}  .... eqn 1

(i) Downstream
 v+3 = \frac{90}{t}

v = \frac{90}{t} - 3  , substituting this in eqn 1

\frac{90-6t}{t} = \frac{180}{2t+1}

(90-6t)(2t+1)= 180t

90=18t

t=5.

where have i gone wrong?

EMPOWERgmatRichC · Answer

Hi GRS,

This equation does NOT 'simplify' in the way that you wrote.

(90-6t)(2t+1)= 180t
 
FOIL it out, combine like terms and then divide by 3... You will end up with 2 solutions (because it's a Quadratic) and the one positive solution is the answer to the original prompt.

GMAT assassins aren't born, they're made,
Rich

CrackverbalGMAT · Answer

Upstream speed = V - 3
Downstream Speed = V + 3

\frac{90}{v-3} - \frac{90}{v+3} = \frac{1}{2}

\frac{90(v+3) - 90(v-3)}{ (v+3)(v-3) }= \frac{1}{2}

\frac{90(v+3-v+3)}{(v^2 -9)} = \frac{1}{2}

90*6 *2 = v^2 -9 
 v^2 = 1080 + 9 = 1089 
v= 33

So the time taken by boat to travel downstream = 90/(v+3) = 90/36 = 2.5 hrs

Option A is the correct answer.

Another approach I would suggest is to try logical elimination of the options.
Most of the cases, V will be an integer. 
so the Downstream speed = V + 3 will also be an integer.
 \frac{90}{Downstream speed }= time  
=> 90/time taken = Downstream Speed
That means, when you divide 90 by the options choices ,you should get an integer as well.

Option A will give an integer .You can also crosscheck by finding Upstream time and see if it is 3 hrs i.e. 2.5 + .5 = 3 hrs
Opt C, D,E can be eliminated as it give a recurring decimal.

Thanks,
 Clifin J Francis
GMAT SME

avigutman · Answer

Normally with this type of question the answer choices will be easy to work backwards from, so it's surprising to see decimals here. 
Here are links to two other official problems of the same type:
 https://gmatclub.com/forum/a-store-currently-charges-the-same-price-for-each-towel-that-144780.html 
 https://gmatclub.com/forum/at-his-regular-hourly-rate-don-had-estimated-the-labor-cost-136642.html

In this case, we're told that the 90 miles take half an hour longer if the speed is 6mph slower. So I would just try answer choice A, because adding half an hour to it gets us an integer.

(A) 90 miles in 3 hours means 30mph, and I must check whether 2.5 * 36mph is also 90 miles. Yes, it is (I check quickly by "borrowing a factor of 4 from the 36 and "giving" it to the 2.5, thereby getting 10*9). So the answer is A.

*it is inappropriate, in my opinion, to solve this problem, or the other two that I linked to, using algebra.

PVOG · Answer

Hey guys, this took me just under 3.5 mins to solve on the Mock Exam GMAT 2 exam, the part that really held me up was the square root of 1089 step.

I have just been reviewing the paper now, and I was wondering how I could've solved this faster, I stupidly just tried numbers and by trial and error I found 33 works (when squared yields 1089).

In hindsight, do you guys think that prime factorisation would have been the most optimal way to root such a large number?

My logic (had I instead used prime factorisation) is that 1089 is divisible by 11 via inspection (1-0+8-9 is divisible by 11, therefore 1089 is), therefore:

1089 = 11*99 = 11*33*3 = 33*33, so the root is 33.

Is this the best way to handle rooting larger numbers on the GMAT in terms of speed / effectiveness? Or is there better?

ThatDudeKnows · Answer

30^2 is 900. 40^2 is 1600. We need something between 30 and 40 that is closer to 30 than to 40 and that, when squared, will have a units digit of 9. 33 sure sounds good to me!

ThatDudeKnows · Answer

As always, I'd approach this problem by making sure to look at the answers in addition to the question right out of the gate. There are only five possible answers and the test writers give them to us before we do any work. Only on of the answer choices is going to give an integer value when we divide it into 90 and only one other is going to give something aside from a repeating decimal. The odds are VERY good that it's going to be A, and in the wonky scenario it's not A, it would be VERY likely to be B. Let's just try A.

The boat travelled 90 miles downstream in 2.5 hours, so 36mph. That means it travelled upstream at 30mph, so it took 3 hours. Is that a half hour longer than downstream? Yep.
Answer choice A.

Remember that business schools and GMAC are trying to test how you think rather than how well you can tackle middle/high school math. The test has TONS of opportunities to use logic in lieu of the math. Getting really good at incorporating the answer choices into your thinking is a HUGE opportunity.

srinigaj · Answer

Why cant you set the distances equal to each other and solve for T?

KarishmaB · Answer

Then you would have two variables, v and t and you will not be using the data that distance is 90. You will not be able to get the value of t. 
Instead you don't want to introduce a new variable and want to use the given data.

Aalto700 · Answer

is this way of drawing the table faster brunel I substituting answer choice 2.5 and 3 first because it seems 90 is divisible by these 2 numbers. Since there are t v-3, v+3, I assumed that v is a integer. Is there a better way of choosing substituting answer choices for speed up? GMAT-Club-Forum-eds36j6b.png

John79 · Answer

Hi,

Why can't we equate the distances, since it is same?

i.e. (v-3) (t+0.5) = (v+3) t What am i missing here?

MartyMurray · Answer

We could. At the same time, without 90 miles specified as the distance, multiple values work for v and t.

(v-3) (t+0.5) = (v+3) t

vt - 3t + 0.5v - 1.5 = vt + 3t

0.5v - 1.5 = 6t

Possible values of v and t:

v = 15 t = 1

v = 27 t = 2

and so on

So, we can save steps by setting it up using 90 from the start, which allows us to use only one variable, v, since t = 90/(v + 3).

A boat traveled upstream 90 miles at an average speed of

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A boat traveled upstream 90 miles at an average speed of

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