A boat traveled upstream \(90\) miles at an average speed of \(v-3\) miles per hour and then traveled the same distance

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A boat traveled upstream \(90\) miles at an average speed of \(v-3\) miles per hour and then traveled the same distance downstream at an average speed of \(v+3\) miles per hour. If the trip upstream took a half-hour longer than the trip downstream, then how many hours did it take the boat to travel downstream?

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1

Answer: A

Source: GMAT Prep

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Gmat_mission wrote:
Sun Apr 11, 2021 3:13 am
A boat traveled upstream \(90\) miles at an average speed of \(v-3\) miles per hour and then traveled the same distance downstream at an average speed of \(v+3\) miles per hour. If the trip upstream took a half-hour longer than the trip downstream, then how many hours did it take the boat to travel downstream?

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1

Answer: A

Source: GMAT Prep
I like to begin with a "word equation."
We can write:
travel time upstream = travel time downstream + 1/2

Time = distance/rate
So, we can replace elements in our word equation to get:
90/(v-3) = 90/(v+3) + 1/2

Now solve for v (lots of work here)
.
.
.
v = 33

So, travel time downstream = 90/(v+3)
= 90/(33+3)
= 90/36
= 5/2
= 2 1/2 hours
Answer: A

Cheers,
Brent
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