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# A boat traveled upstream a certain distance and then

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A boat traveled upstream a certain distance and then  [#permalink]

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26 Jun 2014, 19:28
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Difficulty:

25% (medium)

Question Stats:

78% (01:44) correct 22% (01:39) wrong based on 134 sessions

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A boat traveled upstream a certain distance and then traveled downstream, a distance which is not the same distance. If the time traveled in both the cases is t hrs, and the speed of the boat is x miles/hr, what is the total distance traveled by the boat?

A. xt miles
B. 3x/2t miles
C. 2xt miles
D. t/3x miles
E. 3xt miles

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A boat traveled upstream a certain distance and then  [#permalink]

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26 Jun 2014, 19:59
1
Let a=rate of the river

$$Distance = Rate*Time$$

$$Distance (Upstream) * Distance (Downstream) = Total Distance$$

$$t(x-a)+t(x+a)=D$$
$$t(x-a+x+a)=D$$
$$2xt=D$$

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Re: A boat traveled upstream a certain distance and then  [#permalink]

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21 Nov 2014, 00:50
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Distance = Speed * Time

$$= xt + xt = 2xt$$

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Re: A boat traveled upstream a certain distance and then  [#permalink]

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30 Jan 2015, 05:46
1
PareshGmat wrote:
Distance = Speed * Time

$$= xt + xt = 2xt$$

Hi Paresh,

I also chose this answer. However, I do have one question:
Why is the rate x and not xt?

Because I thought that since the boat is doing x miles in one hour, we need to find how many miles it will do in t hours. So, it would do xt miles in t hours, making the rate xt. This ends in an answer 2xt^2. This doesn't exist in the answer choices and made me think that my rate must have an extra x which is caused the square, so I chose the correct answer.

It would be great if you could explain this to me though!
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Re: A boat traveled upstream a certain distance and then  [#permalink]

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30 Jan 2015, 13:32
Hi All,

This question can be solved by TESTing VALUES.

**NOTE: The prompt states that the distance traveled upstream and downstream is NOT the same distance. This implies that the stream itself is effecting the speed of the boat. We have to factor that in to our calculations, so I will be TESTing a VALUE for the speed of the stream too.

T = Time = 2 hours in each direction
X = Boat Speed = 10 miles/hour
Stream Speed = 1 mile/hour

Upstream:
D = (R)(T)
D = (10-1)(2) = 18 miles

Downstream:
D = (R)(T)
D = (10+1)(2) = 22 miles

Total Distance = 18 + 22 = 40 miles

So, we're looking for an answer that = 40, when T=2 and X = 10

Answer A: XT = (10)(2) = 20 NOT a match
Answer B: 3X/2T = (3)(10)/(2)(2) = 30/4 = 7.5 NOT a match
Answer C: 2XT = 2(10)(2) = 40 This IS a MATCH
Answer D: T/3X = 2/30 = 1/5 NOT a match
Answer E: 3XT = (3)(10)(2) = 60 NOT a match

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A boat traveled upstream a certain distance and then  [#permalink]

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30 Jan 2015, 19:17
1
1
PareshGmat wrote:
Distance = Speed * Time

$$= xt + xt = 2xt$$

hi ,
although the ans is correct as the question is in its simplest form,
you cant take the dist xt on both cases as it is given distance is not the same..
pl add or subtract the speed of stream in downstream/upstream..
if time and speed is same, it means the boat has travelled more distance downstream than upstream..
take speed of boat =b mph.. resultant speed upstream and downstream=(x-b) and (x+b)...
time taken is same t so distance=(x-b)t+ (x+b)t=2xt ans C
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Re: A boat traveled upstream a certain distance and then  [#permalink]

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30 Jan 2015, 19:23
pacifist85 wrote:
PareshGmat wrote:
Distance = Speed * Time

$$= xt + xt = 2xt$$

Hi Paresh,

I also chose this answer. However, I do have one question:
Why is the rate x and not xt?

Because I thought that since the boat is doing x miles in one hour, we need to find how many miles it will do in t hours. So, it would do xt miles in t hours, making the rate xt. This ends in an answer 2xt^2. This doesn't exist in the answer choices and made me think that my rate must have an extra x which is caused the square, so I chose the correct answer.

It would be great if you could explain this to me though!

hi pacifist, it is given that rate is x, so you cant take it as xt because multiplying by t makes it distance..
rate,x, is in miles/hour and time,t, is in hour..
so xt will be in miles/hour*hour=miles, which has to be unit of distance...
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Re: A boat traveled upstream a certain distance and then  [#permalink]

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31 Jan 2015, 22:54
chetan2u wrote:
pacifist85 wrote:
PareshGmat wrote:
Distance = Speed * Time

$$= xt + xt = 2xt$$

Hi Paresh,

I also chose this answer. However, I do have one question:
Why is the rate x and not xt?

Because I thought that since the boat is doing x miles in one hour, we need to find how many miles it will do in t hours. So, it would do xt miles in t hours, making the rate xt. This ends in an answer 2xt^2. This doesn't exist in the answer choices and made me think that my rate must have an extra x which is caused the square, so I chose the correct answer.

It would be great if you could explain this to me though!

hi pacifist, it is given that rate is x, so you cant take it as xt because multiplying by t makes it distance..
rate,x, is in miles/hour and time,t, is in hour..
so xt will be in miles/hour*hour=miles, which has to be unit of distance...

That's correct. Rate or Speed is the same thing which is given in the question
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Re: A boat traveled upstream a certain distance and then  [#permalink]

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22 Feb 2019, 08:53
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Re: A boat traveled upstream a certain distance and then   [#permalink] 22 Feb 2019, 08:53
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