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

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

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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
[Reveal] Spoiler: OA

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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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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
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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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New post 28 Jan 2016, 23:55
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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.

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[Reveal] Spoiler:
C


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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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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 \(D1 = R1*T1 = 24*4 = 96\)
Answer is C
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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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New post 24 Jun 2017, 19:02
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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New post 24 Jun 2017, 19:50
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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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

Let's start with a word equation....

(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

Answer: C

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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New post 22 Dec 2017, 09:31
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

Let's start with a word equation....

(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

Answer: C

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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New post 07 Apr 2018, 23:59
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.
Re: The current in a river is 4 mph. A boat can travel 20 mph in still wat   [#permalink] 07 Apr 2018, 23:59
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