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• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # 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 Joined: 02 Sep 2009 Posts: 52108 The current in a river is 4 mph. A boat can travel 20 mph in still wat [#permalink] ### Show Tags 24 Jan 2016, 05:38 2 19 00:00 Difficulty: 35% (medium) Question Stats: 75% (02:02) correct 25% (01:55) wrong based on 403 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 Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood. Joined: 30 Jul 2013 Posts: 323 Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat [#permalink] ### Show Tags 24 Jan 2016, 06:48 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 Answer: C EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13325 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 28 Jan 2016, 22:55 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. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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24 Jun 2017, 14:39
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 $$D1 = R1*T1 = 24*4 = 96$$
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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24 Jun 2017, 18:02
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
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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24 Jun 2017, 18:50
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.
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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05 Dec 2017, 08:28
1
Top Contributor
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
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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22 Dec 2017, 08:31
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".
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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07 Apr 2018, 22:59
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.
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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08 Dec 2018, 12:36
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
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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat  [#permalink]

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08 Dec 2018, 13:13
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.

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Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat &nbs [#permalink] 08 Dec 2018, 13:13
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