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The speed of a boat is 5 times the speed at which a river flows. What

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The speed of a boat is 5 times the speed at which a river flows. What  [#permalink]

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New post 17 Jan 2019, 01:10
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[Math Revolution GMAT math practice question]

The speed of a boat is \(5\) times the speed at which a river flows. What percent of the time it takes for the boat to travel down the river (i.e. in the same direction as the river flow) does it take for the boat to travel up the river?

\(A. 50%\)
\(B. 80%\)
\(C. 100%\)
\(D. 150%\)
\(E. 200%\)

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The speed of a boat is 5 times the speed at which a river flows. What  [#permalink]

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New post 17 Jan 2019, 01:19
Let the speed of the river be - x.
Let the speed of the boat be - 5x.

Let D be the distance the boat travels Upstream and Downstream.
Time taken for downstream = \(\frac{D}{5x+x}\) = \(\frac{D}{6x}\)
Time taken for upstream = \(\frac{D}{5x-x}\) = \(\frac{D}{4x}\)

\(\frac{D}{4x}\)*\(\frac{6x}{D}\) = 1.5*100 = 150.
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Re: The speed of a boat is 5 times the speed at which a river flows. What  [#permalink]

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New post 17 Jan 2019, 02:05
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The speed of a boat is \(5\) times the speed at which a river flows. What percent of the time it takes for the boat to travel down the river (i.e. in the same direction as the river flow) does it take for the boat to travel up the river?

\(A. 50%\)
\(B. 80%\)
\(C. 100%\)
\(D. 150%\)
\(E. 200%\)



let speed of river = 10
speed of boat = 5*10 = 50
downstream speed = 10+50 = 60
upstream speed = 50-10 = 40

time of upstream = distance / speed upstream
time of down stream = distance / speed downstream

let distance be x
so
time up/ time down = speed down/ speed down = 60 /40 = 1.5 = 150 %
IMO D
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Re: The speed of a boat is 5 times the speed at which a river flows. What  [#permalink]

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New post 17 Jan 2019, 03:38
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The speed of a boat is \(5\) times the speed at which a river flows. What percent of the time it takes for the boat to travel down the river (i.e. in the same direction as the river flow) does it take for the boat to travel up the river?

\(A. 50%\)
\(B. 80%\)
\(C. 100%\)
\(D. 150%\)
\(E. 200%\)

\(? = {{{T_{{\rm{up}}}}} \over {{T_{{\rm{down}}}}}}\)

\({V_r} = {{1\,\,{\rm{m}}} \over {1\,\,\sec }}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{V_b} = {{5\,\,{\rm{m}}} \over {1\,\,\sec }}\)

\({\rm{distance}} = 12\,{\rm{m}}\)


\(\left. \matrix{
{\rm{down}}\,\,{\rm{:}}\,\,\,{\rm{12}}\,{\rm{m}}\,\,\left( {{{1\,\,\sec } \over {5 + 1\,\,{\rm{m}}}}} \right) = \,\,\,2\,\,\sec \,\,\, = \,\,\,{T_{{\rm{down}}}} \hfill \cr
{\rm{up}}\,\,{\rm{:}}\,\,\,{\rm{12}}\,{\rm{m}}\,\,\left( {{{1\,\,\sec } \over {5 - 1\,\,{\rm{m}}}}} \right) = \,\,\,3\,\,\sec \,\,\, = \,\,\,{T_{{\rm{up}}}} \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \,\,{3 \over 2}\,\, = \,\,150\%\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: The speed of a boat is 5 times the speed at which a river flows. What  [#permalink]

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New post 17 Jan 2019, 05:57
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The speed of a boat is \(5\) times the speed at which a river flows. What percent of the time it takes for the boat to travel down the river (i.e. in the same direction as the river flow) does it take for the boat to travel up the river?

\(A. 50%\)
\(B. 80%\)
\(C. 100%\)
\(D. 150%\)
\(E. 200%\)


Let x = the speed of the river (in miles per hour)
So, 5x = the speed of the boat in (miles per hour)
Let d = distance traveled (in miles)

This means the boat's speed going UPriver = 5x - x = 4x
And the boat's speed going DOWNriver = x + 5x = 6x

time = distance/speed
So, travel time going UPriver = d/4x
So, travel time going DOWNriver = d/6x

What percent of the time it takes for the boat to travel DOWNriver does it take for the boat to travel UPriver?
We must take the fraction (d/4x)/(d/6x), and convert it to a PERCENT

(d/4x)/(d/6x) = (d/4x)(6x/d)
= 6xd/4xd
= 6/4
= 3/2
= 150/100
= 150%

Answer: D

Cheers,
Brent
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Re: The speed of a boat is 5 times the speed at which a river flows. What  [#permalink]

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New post 20 Jan 2019, 17:41
=>

Let \(d\) and \(v\) be the distance the boat travels and the speed of the river flow, respectively.
The time the boat takes to travel up the river is \(\frac{d}{( 5v – v )} = \frac{d}{4v}\).
The time the boat takes to travel down the river is \(\frac{d}{( 5v + v )} = \frac{d}{6v}\).
Let \(p\) be the percentage are looking for.
Using the IVY approach, we obtain \(\frac{d}{4v} = p(\frac{1}{100})(\frac{d}{6v})\) or \(p = (\frac{6}{4})*100 = 150(%).\)

Therefore, the answer is D.
Answer: D
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Re: The speed of a boat is 5 times the speed at which a river flows. What   [#permalink] 20 Jan 2019, 17:41
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