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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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue May 04, 2021 6:43 am

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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

Source: Beat The GMAT — Problem Solving | Tue May 04, 2021 6:43 am

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Re: A boat traveled upstream $90$ miles at an average speed of $v-3$ miles per hour and then traveled the same dista

by Brent@GMATPrepNow » Wed May 05, 2021 6:44 am

VJesus12 wrote: ↑
Tue May 04, 2021 6:43 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

Brent Hanneson - Creator of GMATPrepNow.com

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