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

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.

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.

=>

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