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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A boat traveled 90 miles upstream at a constant speed and then travele

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Intern  B
Joined: 19 May 2019
Posts: 5
A boat traveled 90 miles upstream at a constant speed and then travele  [#permalink]

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4 00:00

Difficulty:   75% (hard)

Question Stats: 58% (03:04) correct 42% (02:51) wrong based on 50 sessions

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A boat traveled 90 miles upstream at a constant speed and then traveled the same distance downstream at a constant speed. If the constant velocity of the water is 3 miles per hour and the whole trip took 12.5 hours, the upstream trip took hour many more hours than the downstream trip?

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Manager  G
Joined: 09 Nov 2015
Posts: 191
Re: A boat traveled 90 miles upstream at a constant speed and then travele  [#permalink]

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1
Let 's' be the upstream speed (US). Then (s+6) is the downstream speed (DS).
Time for the return trip=US time + DS time...> (25/2) hrs = 90/s + 90/(s+6)...> 5s^2 - 42s - 216 = 0....> 5s^2 - 60s + 18s - 216...> 5s(s-12) + 18(s-12)...> (s-12)(s+18)=0...> s=12
US time - DS time = 90/12 - 90/18 = 2.5 hrs. ANS: D
Target Test Prep Representative V
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Re: A boat traveled 90 miles upstream at a constant speed and then travele  [#permalink]

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1
GOHOSATRAJIT wrote:
A boat traveled 90 miles upstream at a constant speed and then traveled the same distance downstream at a constant speed. If the constant velocity of the water is 3 miles per hour and the whole trip took 12.5 hours, the upstream trip took hour many more hours than the downstream trip?

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

We can let the speed of the boat in still water be r and create the equation:

90/(r - 3) + 90/(r + 3) = 12.5

Multiplying the equation by (r -3)(r + 3), or r^2 - 9, we have:

90(r + 3) + 90(r - 3) = 12.5(r^2 - 9)

90r + 270 + 90r - 270 = 12.5r^2 - 112.5

180r = 12.5r^2 - 112.5

Multiplying by 2, we have:

360r = 25r^2 - 225

Dividing by 5, we have:

5^2 - 72r - 45 = 0

(5r + 3)(r - 15) = 0

r = -3/5 or r = 15

Since r can’t be negative, r = 15. Therefore, it takes the boat 90/(15 - 3) = 90/12 = 7.5 hours to travel upstream and 90/(15 + 3) = 90/18 = 5 hours to travel downstream. So it takes 7.5 - 5 = 2.5 more hours to travel upstream than downstream.

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Manager  B
Joined: 02 Nov 2018
Posts: 55
Re: A boat traveled 90 miles upstream at a constant speed and then travele  [#permalink]

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ScottTargetTestPrep wrote:
GOHOSATRAJIT wrote:
A boat traveled 90 miles upstream at a constant speed and then traveled the same distance downstream at a constant speed. If the constant velocity of the water is 3 miles per hour and the whole trip took 12.5 hours, the upstream trip took hour many more hours than the downstream trip?

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

We can let the speed of the boat in still water be r and create the equation:

90/(r - 3) + 90/(r + 3) = 12.5

Multiplying the equation by (r -3)(r + 3), or r^2 - 9, we have:

90(r + 3) + 90(r - 3) = 12.5(r^2 - 9)

90r + 270 + 90r - 270 = 12.5r^2 - 112.5

180r = 12.5r^2 - 112.5

Multiplying by 2, we have:

360r = 25r^2 - 225

Dividing by 5, we have:

5^2 - 72r - 45 = 0

(5r + 3)(r - 15) = 0

r = -3/5 or r = 15

Since r can’t be negative, r = 15. Therefore, it takes the boat 90/(15 - 3) = 90/12 = 7.5 hours to travel upstream and 90/(15 + 3) = 90/18 = 5 hours to travel downstream. So it takes 7.5 - 5 = 2.5 more hours to travel upstream than downstream.

How did you assume the boat's speed upstream and downstream is constant? Surely if this was the case the question would've said "at the same constant speed"..
CEO  V
Joined: 03 Jun 2019
Posts: 2909
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
A boat traveled 90 miles upstream at a constant speed and then travele  [#permalink]

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GOHOSATRAJIT wrote:
A boat traveled 90 miles upstream at a constant speed and then traveled the same distance downstream at a constant speed. If the constant velocity of the water is 3 miles per hour and the whole trip took 12.5 hours, the upstream trip took hour many more hours than the downstream trip?

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

Given:
1. A boat traveled 90 miles upstream at a constant speed and then traveled the same distance downstream at a constant speed.
2. The constant velocity of the water is 3 miles per hour.
3. The whole trip took 12.5 hours.

Asked: Upstream trip took hour many more hours than the downstream trip?

Let the speed on the boat be v kmh

90/(v-3) + 90/(v+3) = 12.5
v = 15 kmh
I got the solution by hit and try but this can be solved using quadratic equations.
90/12 + 90/18 = 7.5 + 5 = 12.5
Upstream trip took hour many more hours than the downstream trip = 7.5 - 5 = 2.5

IMO D
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com A boat traveled 90 miles upstream at a constant speed and then travele   [#permalink] 19 Aug 2019, 03:44

# A boat traveled 90 miles upstream at a constant speed and then travele  