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

Question

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

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

ScottTargetTestPrep · Accepted Answer

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:

5r^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

effatara · Answer

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

jamalabdullah100 · Answer

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"..

Kinshook · Answer

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

GMATGuruNY · Answer

The constant velocity of the water is 3 miles per hour. 
Since the current INCREASES the downstream speed by 3 mph and DECREASES the upstream speed by 3 mph, the DIFFERENCE between the two speeds = 6 mph.

The whole trip took 12.5 hours. 
Let U = the upstream time and D = the downstream time.
Since the trip took a total time of 12.5 hours, we get:
U+D = 12.5

The upstream trip took how many more hours than the downstream trip? 
We can PLUG IN THE ANSWERS, which represent the value of U-D.
When the correct answer is plugged in, the difference between the two speeds = 6.

D: U-D = 2.5
Adding together U+D = 12.5 and U-D = 2.5, we get:
2U = 15
U=7.5, implying that D=5
Downstream speed - upstream speed  = \frac{90}{5} - \frac{90}{7.5} = 18 - 12 = 6 
Success!

D

arushi118 · Answer

let speed of boat = v.
90/(v-3) + 90/(v+3) = 12.5
On solving we get v = 15

So, to find the diff in time:
90/18 - 90/12
=2.5

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards