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

 It is currently 22 Oct 2019, 23:26 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  The current in a river is 4 mph. A boat can travel 20 mph in still wat

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58436
The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

2
20 00:00

Difficulty:   35% (medium)

Question Stats: 75% (02:23) correct 25% (02:17) wrong based on 451 sessions

HideShow timer Statistics

The current in a river is 4 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

A. 69 miles
B. 88 miles
C. 96 miles
D. 100 miles
E. 112 miles

_________________
Retired Moderator B
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 300
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

2
Upstream Speed = 20-4=16 mph
Downstream Speed = 20+4 = 24 mph

D/16 + D/24 = 10 hours
Solving for D we get D=96

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15314
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

2
Hi All,

This question is a multi-step rate question, so you'll need to use the Distance Formula, but you can actually go about solving it in a couple of different ways.

From the prompt, we know that the rate "with" the current is 24 miles/hour and the rate "against" the current is 16 miles/hour. Since 24/16 = 1.5, there's an interesting way to convert this information into a 'unit' that we can use to our advantage...

IF...we traveled upstream for 24 miles, then downstream for 24 miles, we would spend....

"with" the current
D = (R)(T)
24 = (24 mph)(T)
1 hour = T

"against" the current
D = (R)(T)
24 = (16 mph)(T)
1.5 hours = T

TOTAL Time = 1 + 1.5 = 2.5 hours to travel 24 miles in each direction. This data is useful, since the question asks how far the boat can travel "with" the current if the TOTAL trip takes 10 hours.

10 hours/2.5 hours = 4 "blocks" of 24 miles

(4)(24) = 96 miles in each direction.

GMAT assassins aren't born, they're made,
Rich
_________________
Manager  S
Joined: 22 Nov 2016
Posts: 202
Location: United States
GPA: 3.4
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

1

Another approach is using the term 'round trip' and equating distances

$$R1*T1 = R2*T2$$
Given $$T1 + T2 = 10$$
Speed upstream is 16 (deduct opposing current)
Speed downstream is 24 (add current)

$$24*T1=16(10-T1)$$
$$T1=4$$

Hence $$D1 = R1*T1 = 24*4 = 96$$
_________________
Kudosity killed the cat but your kudos can save it.
VP  P
Joined: 07 Dec 2014
Posts: 1224
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

Bunuel wrote:
The current in a river is 4 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

A. 69 miles
B. 88 miles
C. 96 miles
D. 100 miles
E. 112 miles

let t=upstream hours
24 mph*(10-t) hours=16t miles
t=6 hours
6 hours*16 mph=96 upstream miles
C
Senior Manager  B
Joined: 28 Jun 2015
Posts: 283
Concentration: Finance
GPA: 3.5
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

Let D be the distance upstream.
D/20-4 + D/20+4 = 10
D(1/16 + 1/24) = 10
D(3+2/48) = 10
D/48 = 2
D = 96.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4018
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

1
Top Contributor
1
Bunuel wrote:
The current in a river is 4 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

A. 69 miles
B. 88 miles
C. 96 miles
D. 100 miles
E. 112 miles

Boat's speed UPSTREAM = 20mph - 4mph = 16mph
Boat's speed DOWNSTREAM = 20mph + 4mph = 24mph

(travel time UPSTREAM) + (travel time DOWNSTREAM) = 10 hours

time = distance/speed
We know the speeds, but not the distance each way
So, let d = distance EACH EACH

Our word equation becomes....
d/16 + d/24 = 10
Eliminate the fractions by multiplying each side by 28 (the least common multiple of 16 and 24)
When we do this, we get: 3d + 2d = 480
Simplify: 5d = 480
Solve: d = 96

So, the distance EACH WAY is 96 miles

Cheers,
Brent
_________________
SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1686
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

GMATPrepNow wrote:
Bunuel wrote:
The current in a river is 4 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

A. 69 miles
B. 88 miles
C. 96 miles
D. 100 miles
E. 112 miles

Boat's speed UPSTREAM = 20mph - 4mph = 16mph
Boat's speed DOWNSTREAM = 20mph + 4mph = 24mph

(travel time UPSTREAM) + (travel time DOWNSTREAM) = 10 hours

time = distance/speed
We know the speeds, but not the distance each way
So, let d = distance EACH EACH

Our word equation becomes....
d/16 + d/24 = 10
Eliminate the fractions by multiplying each side by 28 (the least common multiple of 16 and 24)
When we do this, we get: 3d + 2d = 480
Simplify: 5d = 480
Solve: d = 96

So, the distance EACH WAY is 96 miles

Cheers,
Brent

I really like your algebraic approach "word equation".
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Intern  B
Joined: 02 Nov 2017
Posts: 17
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

Bunuel wrote:
The current in a river is 4 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

A. 69 miles
B. 88 miles
C. 96 miles
D. 100 miles
E. 112 miles

another way to solve the problem would be to think a little logically here.

We know that the distance upstream and the distance downstream is the same. therefore, upstream=downstream (eq1)

Also, if total time is 10, then assuming Upstream as T, Downstream will be 10-T. (Not T-10 since 10 is the total)

Using R*T=D formula we then get,
Upstream= 16*T=D (eq2)
Downstream= 24*(10-T)=D (eq3)

Now Using eq1 we get eq2=eq3. Solving that,

16t=24(10-t)
16t=240-24t
40t=240
t=6

substituting t=6 in the Upstream equation eq2 we get 96.

To verify, we can also substitute in eq3 which should also give 96.

Hope it helps.
Intern  B
Joined: 20 Mar 2018
Posts: 1
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

Hi,
shouldn't it be 192 as the stem asked about the distance of the round trip? A - B & B - A so in this way total distance should be 2D. I have done it with a tabular form. I saw the speed in the ration 6:4 so time would be 4:6. and then found the D as 96 and the total distance of the round trip to be 192.
Thanks Bunuel sriharimurthy
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15314
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

Show Tags

1
ashish0027 wrote:
Hi,
shouldn't it be 192 as the stem asked about the distance of the round trip? A - B & B - A so in this way total distance should be 2D. I have done it with a tabular form. I saw the speed in the ration 6:4 so time would be 4:6. and then found the D as 96 and the total distance of the round trip to be 192.
Thanks Bunuel sriharimurthy

Hi ashish0027,

The prompt does NOT ask for the distance of the round-trip; it asks how far the boat can go 'up river' (meaning in just one direction). It takes 10 hours total to 'up river' and THEN back 'down river', but again - the question is not asking about the round-trip.

GMAT assassins aren't born, they're made,
Rich
_________________ Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat   [#permalink] 08 Dec 2018, 14:13
Display posts from previous: Sort by

The current in a river is 4 mph. A boat can travel 20 mph in still wat

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  