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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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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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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 675 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) The speed of a boat is 5 times the speed at which a river flows. What [#permalink] Show Tags 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. _________________ Press +1 Kudo If my post helps! SVP Joined: 18 Aug 2017 Posts: 1899 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: The speed of a boat is 5 times the speed at which a river flows. What [#permalink] Show Tags 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 _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 764 Re: The speed of a boat is 5 times the speed at which a river flows. What [#permalink] Show Tags 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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net CEO Joined: 11 Sep 2015 Posts: 3442 Location: Canada Re: The speed of a boat is 5 times the speed at which a river flows. What [#permalink] Show Tags 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 _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6978 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The speed of a boat is 5 times the speed at which a river flows. What [#permalink] Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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