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

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3 00:00

Difficulty:   65% (hard)

Question Stats: 55% (02:51) correct 45% (02:46) wrong based on 33 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  S
Joined: 09 Nov 2015
Posts: 107
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
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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.

Answer: D
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Intern  B
Joined: 02 Nov 2018
Posts: 35
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.

Answer: D

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"..
Director  P
Joined: 03 Jun 2019
Posts: 955
Location: India
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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E-mail : kinshook.chaturvedi@gmail.com A boat traveled 90 miles upstream at a constant speed and then travele   [#permalink] 19 Aug 2019, 04:44
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