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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## The speed of a boat is 5 times the speed at which a river fl tagged by: Max@Math Revolution ##### This topic has 5 expert replies and 0 member replies ### GMAT/MBA Expert ## The speed of a boat is 5 times the speed at which a river fl ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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% _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™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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Max@Math Revolution 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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Max@Math Revolution 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%

Cheers,
Brent

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Max@Math Revolution 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 the river's rate = 1 mph and the boat's rate = 5 mph.

When the boat travels DOWNRIVER, the boat and the river WORK TOGETHER, so we ADD their rates:
5+1 = 6 mph.
When the boat travels UPRIVER, the boat and the river COMPETE, so we SUBTRACT their rates:
5-1 = 4 mph.

Rate and time have a RECIPROCAL relationship.
Since the rate upriver is 4/6 of the rate downriver, the time upriver is 6/4 of the time downriver:
6/4 * 100 = 150%.

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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 d / ( 5v - v ) = d/4v.
The time the boat takes to travel down the river is d / ( 5v + v ) = d/6v.
Let p be the percentage are looking for.
Using the IVY approach, we obtain d/4v = p(1/100)(d/6v) or p = (6/4)*100 = 150(%).

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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 Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2424 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution 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% We can let the current of the river be 2 mph. Thus the speed of the boat is 5 x 2 = 10 mph. Furthermore, when the boat travels with the current, its speed is 10 + 2 = 12 mph, but when it travels against the current, its speed is 10 - 2 = 8 mph. Letâ€™s let the length of the river be 24 miles. It will take the boat 24/12 = 2 hours when it travels with the current and 24/8 = 3 hours when it travels against the current. Therefore, the time it takes for the boat to travel up the river (i.e., against the current) is 3/2 = 150% of the time it takes for the boat to travel down the river (i.e., with the current). Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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