Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 22:02

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A man travels by a motor boat down a river to his office and back

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 May 2010
Posts: 162
A man travels by a motor boat down a river to his office and back  [#permalink]

### Show Tags

19 Jun 2019, 00:06
2
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:39) correct 44% (03:02) wrong based on 18 sessions

### HideShow timer Statistics

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is:

A) 6^0.5 : 2^0.5
B) 7^0.5 : 2^0.5
C) 2 x 5^0.5 : 3^0.5
D) 3:2
E) 7^0.5 : 2
Manager
Joined: 07 Aug 2017
Posts: 79
Location: India
GPA: 4
WE: Information Technology (Consulting)
Re: A man travels by a motor boat down a river to his office and back  [#permalink]

### Show Tags

19 Jun 2019, 02:22
prashanths wrote:
A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is:

A) 6^0.5 : 2^0.5
B) 7^0.5 : 2^0.5
C) 2 x 5^0.5 : 3^0.5
D) 3:2
E) 7^0.5 : 2

Let $$Sb$$ be the speed of boat and $$Sr$$ be the speed of river.
When the man is travelling downstream, his speed is = $$Sb + Sr$$
and when he is travelling upstream, his speed is = $$Sb - Sr$$

The average speed of both upstream and downstream is:
$$\frac{(2*(Sb+Sr)(Sb-Sr))}{(Sb+Sr+Sb-Sr)}$$

$$=\frac{(Sb^2-Sr^2)}{Sb}$$

Let D be the distance and t be the time

$$\frac{(Sb^2-Sr^2)}{Sb} = \frac{D}{t}$$

When the speed of boat is doubled -
Downstream speed = $$2Sb+Sr$$
Upstream speed = $$2Sb-Sr$$

Average speed = $$\frac{2*(4Sb^2-Sr^2)}{4Sb}$$

$$t1=0.25t$$
Distance will remain same.

$$\frac{(4Sb^2-Sr^2)}{2Sb} = \frac{D}{0.25t}$$

$$\frac{(4Sb^2-Sr^2)}{8Sb} = \frac{D}{t}$$

Equating the two equations -

$$\frac{(Sb^2-Sr^2)}{Sb} = \frac{(4Sb^2-Sr^2)}{8Sb}$$

$$8*(Sb^2-Sr^2) = 4Sb^2-Sr^2$$
$$4Sb^2 = 7Sr^2$$
$$Sb^2/Sr^2 = 7/4$$
$$Sb/Sr = 7^\frac{1}{2}/2$$

-----------------------------------------------------------------------
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6967
Location: United States (CA)
Re: A man travels by a motor boat down a river to his office and back  [#permalink]

### Show Tags

21 Jun 2019, 11:57
prashanths wrote:
A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is:

A) 6^0.5 : 2^0.5
B) 7^0.5 : 2^0.5
C) 2 x 5^0.5 : 3^0.5
D) 3:2
E) 7^0.5 : 2

We can let b = the normal speed of the boat and r = the speed of the river. Thus, we need to determine b/r. Furthermore, we can let d = the one-way distance and t = total time when the boat is traveling at its normal speed. We can create the equations:

d/(b + r) + d/(b - r) = t

and

d/(2b + r) + d/(2b - r) = t/4

Multiplying the second equation by 4, we have:

4d/(2b + r) + 4d/(2b - r) = t

Now equating this with the first equation, we have:

d/(b + r) + d/(b - r) = 4d/(2b + r) + 4d/(2b - r)

Dividing the equation by d, we have:

1/(b + r) + 1/(b - r) = 4/(2b + r) + 4/(2b - r)

(b - r + b + r)/[(b + r)(b - r)] = (8b - 4r + 8b + 4r)/[(2b + r)(2b - r)]

2b/(b^2 - r^2) = 16b/(4b^2 - r^2)

Dividing both sides by 2b, we have:

1/(b^2 - r^2) = 8/(4b^2 - r^2)

4b^2 - r^2 = 8b^2 - 8r^2

7r^2 = 4b^2

7/4 = b^2/r^2

√(7/4) = b/r

b/r = √(7)/2

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: A man travels by a motor boat down a river to his office and back   [#permalink] 21 Jun 2019, 11:57
Display posts from previous: Sort by