GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Mar 2019, 11:10

### 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

# It takes 3.5 hours for Mathew to row a distance of X miles

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 24 Mar 2011
Posts: 350
Location: Texas
It takes 3.5 hours for Mathew to row a distance of X miles  [#permalink]

### Show Tags

24 Apr 2011, 13:16
3
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:48) correct 41% (01:30) wrong based on 55 sessions

### HideShow timer Statistics

It takes 3.5 hours for Mathew to row a distance of X miles up the stream. Find his speed in still water.

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1789

### Show Tags

24 Apr 2011, 13:37
agdimple333 wrote:
It takes 3.5 hours for Mathew to row a distance of X miles up the stream. Find his speed in still water.

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.

Sol:
Speed of Matt in still water= $$v_m$$
Speed of Stream= $$v_s$$

As per the stem:
$$\frac{X}{v_m-v_s}=3.5$$-------1

Q: $$v_m=?$$

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

$$\frac{X}{v_m+v_s}=2.5$$ -------2

Equating 1 and 2:
$$3.5(v_m-v_s)=2.5(v_m+v_s)$$
$$3.5v_m-3.5v_s=2.5v_m+2.5v_s$$
$$v_m=6v_s$$-------------3

We now know that Matt's speed is 6 times that of the speed of the stream. But, we don't know the exact value yet.
Not Sufficient.

(2) He can cover a distance of 84 miles downstream in 6 hours.

$$\frac{84}{v_m+v_s}=6$$
$$\frac{84}{6}=v_m+v_s$$
$$v_m+v_s=14$$-----------4

We know the combined speed of Matt and the stream is 14 m/h
Not Sufficient.

Combining both;

Substituting 3 in 4:

$$v_m+\frac{v_m}{6}=14$$
$$7v_m=14*6$$
$$v_m=2*6=12 m/h$$

Sufficient.

Ans: "C"
_________________
Retired Moderator
Joined: 16 Nov 2010
Posts: 1402
Location: United States (IN)
Concentration: Strategy, Technology

### Show Tags

24 Apr 2011, 19:03
D/(V-x) = 3.5

(1) says

D/(V+x) = 2.5

Which is clearly insufficient

(2) says

84/(V+x) = 6

Which is clearly insufficient

(1) and (2) combined

D can be found, and thereafter (V-x) can be found, and finally V and x can be found.

_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Senior Manager
Status: Up again.
Joined: 31 Oct 2010
Posts: 488
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42

### Show Tags

25 Apr 2011, 10:29
agdimple333 wrote:
It takes 3.5 hours for Mathew to row a distance of X miles up the stream. Find his speed in still water.

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.

Speed of boat in still water is the average of Upstream speed and Downstream speed.

So, to calculate speed in still water, we will need to know both upstrem and downstrem speeds.

Statement 1: Time taken to cover distance downstream= 2.5.

There is a relationship between time and speed in Upstream/ Downstream problems. it goes:

$$\frac{Time Taken To Cover Downstream Distance}{Time Taken To Cover Upstream Distance} = \frac{Upstream Speed}{Downstream Speed}$$

So from this statement, we have: $$\frac{2.5}{3.5}= \frac{US}{DS}$$ (US= upstream speed, DS=downstream speed)
It follows: $$5DS=7US$$. Therefore $$US= \frac{5}{7} DS$$.
Since we only have ratios and not actual values, this statement alone is insufficient.

Statement 2: We can calculate downstream speed using this information. Which equals $$\frac{84}{6}= 14mph$$.

However, this doesn't give any info on the Upstream speed, so this statement alone is insufficient.

Combining (1) and (2), we can find out US= $$\frac{5}{7}*14= 10mph.$$

Now we have sufficient information to calculate speed of boat in still water: average of 10 and 14 that is 12 mph.

$$Answer : C$$
_________________
My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html
Non-Human User
Joined: 09 Sep 2013
Posts: 10207
Re: It takes 3.5 hours for Mathew to row a distance of X miles  [#permalink]

### Show Tags

21 Oct 2018, 21:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: It takes 3.5 hours for Mathew to row a distance of X miles   [#permalink] 21 Oct 2018, 21:31
Display posts from previous: Sort by