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The speed of a boat is 5 times the speed at which a river fl

by Max@Math Revolution » Thu Jan 17, 2019 12:54 am

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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 fl

by fskilnik@GMATH » Thu Jan 17, 2019 3:23 am
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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by Brent@GMATPrepNow » Thu Jan 17, 2019 5:45 am
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%

Answer: D

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by GMATGuruNY » Thu Jan 17, 2019 10:15 am
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%.

The correct answer is D.
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by Max@Math Revolution » Sun Jan 20, 2019 5:25 pm
=>

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(%).

Therefore, the answer is D.
Answer: D
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by Scott@TargetTestPrep » Mon Jan 21, 2019 5:56 pm
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.

Let'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

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