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

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%

Chethan92 · Answer

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.

Archit3110 · Answer

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

fskilnik · Answer

? = {{{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.

BrentGMATPrepNow · Answer

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

MathRevolution · Answer

=>

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

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