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In a given river, the current is 6 mph. A certain riverboat can travel

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In a given river, the current is 6 mph. A certain riverboat can travel [#permalink]

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In a given river, the current is 6 mph. A certain riverboat can travel 18 mph in still water. How far upstream (against the current) can the boat travel if a round trip is to take 10 hours?

A) 24

B) 48

C) 60

D) 80

E) 96
[Reveal] Spoiler: OA

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Re: In a given river, the current is 6 mph. A certain riverboat can travel [#permalink]

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New post 23 Sep 2017, 05:05
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HKD1710 wrote:
In a given river, the current is 6 mph. A certain riverboat can travel 18 mph in still water. How far upstream (against the current) can the boat travel if a round trip is to take 10 hours?

A) 24

B) 48

C) 60

D) 80

E) 96


The upstream speed = the boat speed - the current speed = 18 - 6 = 12 mph;
The downstream speed = the boat speed + the current speed = 18 + 6 = 24 mph.

Since the downstream speed of the boat is twice that of the upstream speed, then travelling downstream would take the boat half the time it would take it to travel upstream: t/2 + t = 10 hours, which gives t = 20/3 hours.

In 20/3 hours, the boat will travel upstream (time)(rate) = 20/3*12 = 80 miles.

Answer: D.
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Re: In a given river, the current is 6 mph. A certain riverboat can travel [#permalink]

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New post 23 Sep 2017, 08:46
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HKD1710 wrote:
In a given river, the current is 6 mph. A certain riverboat can travel 18 mph in still water. How far upstream (against the current) can the boat travel if a round trip is to take 10 hours?

A) 24
B) 48
C) 60
D) 80
E) 96


Here's a different approach...

Let d = distance traveled upstream
So, d = distance traveled downstream

The upstream speed = the boat speed - the current speed = 18 - 6 = 12 mph
The downstream speed = the boat speed + the current speed = 18 + 6 = 24 mph.

Let's start with a "word equation"
(time spent traveling upstream) + (time spent traveling downstream) = 10 hours
time = distance/speed
We get: d/12 + d/24 = 10
Multiply both sides by 24 to get: 2d + d = 240
Simplify: 3d = 240
Solve: d = 80

Answer:
[Reveal] Spoiler:
D


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In a given river, the current is 6 mph. A certain riverboat can travel [#permalink]

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New post 23 Sep 2017, 11:19
HKD1710 wrote:
In a given river, the current is 6 mph. A certain riverboat can travel 18 mph in still water. How far upstream (against the current) can the boat travel if a round trip is to take 10 hours?

A) 24

B) 48

C) 60

D) 80

E) 96

Another approach: set distances equal. The boat covers the same distance on both legs of the trip.

D = r*t for each leg of the trip (r = speed)

Upstream speed: (still water speed) - (speed of current)

Downstream speed: (still water speed) + (speed of current)

Total time is 10 hours.
If one leg's time = t, other leg's = (10 - t)

Upstream leg
Speed (rate) = (18-6) = 12
Time = t
Distance = r*t = 12t

Downstream leg
Speed (rate) = (18+6) = 24
Time = (10 - t)
Distance = r*t = 24(10 - t)

D = D
12t = 24(10-t)
12t = 240 - 24t
Divide by 12:
t = 20 - 2t
3t = 20
t = \(\frac{20}{3}\)

How far upstream can the boat travel? rt = D

12 * \(\frac{20}{3}\) = 80

Answer D

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Re: In a given river, the current is 6 mph. A certain riverboat can travel [#permalink]

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New post 24 Sep 2017, 00:16
let x be the distance for a single trip; hence for a round trip, the distance would be 2x
speed of current= 6 mph
speed of boat= 18 mph

speed of boat in upstream= speed of boat - speed of current
speed of boat in upstream= 18-6= 12 mph

speed of boat in downstream= speed of boat +speed of current
speed of boat in downstream= 18+6= 24 mph

total time required= time required to travel upstream + time required to travel downstream
10= x/12 + x/24
10= 2x+x/24
10*24 = 3x
x= 80 miles.

Hence Answer is option D.

Kudos if it helps.

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Re: In a given river, the current is 6 mph. A certain riverboat can travel   [#permalink] 24 Sep 2017, 00:16
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