speed rate question, please help

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cookiemonster26: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Thu Aug 16, 2007 9:49 am; Thanked: 1 times

by cookiemonster26 » Sun Dec 21, 2008 11:54 am

hi Guys,

was hoping if someone could help me out with this question

At full speed, a motorboat can go upstream 10 miles in 15 minutes, and downstream 10 miles in 9 minutes, at full speed, how long will it take the boat to go 10 miles with no current?

correct answer : 45/4 minutes

====

thanks.

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Source: Beat The GMAT — Problem Solving | Sun Dec 21, 2008 11:54 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 21, 2008 12:42 pm

At full speed, a motorboat can go upstream 10 miles in 15 minutes, and downstream 10 miles in 9 minutes, at full speed, how long will it take the boat to go 10 miles with no current?

correct answer : 45/4 minutes

Let boat's speed = B
Let current's speed = C
Calculate the speed of the trip upstream (40 mph) and downstream (200/3 mph)

This gives us two equations

Upstream speed: B - C = 40
Downstream speed: B + C = 200/3
Solve system to get --> B=160/3 mph

Time to travel 10 miles with no current = distance/speed = 10/(160/3) =30/160 hours = 3/16 hours
Multiply by 60 to get # of minutes --> 180/16 minutes = 45/4 minutes.
Phew!

Brent Hanneson - Creator of GMATPrepNow.com

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cookiemonster26: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Thu Aug 16, 2007 9:49 am; Thanked: 1 times

by cookiemonster26 » Sun Dec 21, 2008 12:54 pm

Thanks Brent...

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Emawk: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sun Nov 23, 2008 11:21 am

by Emawk » Sun Dec 21, 2008 1:33 pm

I did this question using pretty much the same approach as Bret, but I got the wrong answer thinking it was 10miles per minute and not 10miles per hour (since it wasn't mentioned in the question). Or is it common sense that I know that whenever they are talking about miles, they always mean it in hours?

I must have done something wrong in my calculations.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Mon Dec 22, 2008 1:48 am

Emawk wrote:I did this question using pretty much the same approach as Bret, but I got the wrong answer thinking it was 10miles per minute and not 10miles per hour (since it wasn't mentioned in the question). Or is it common sense that I know that whenever they are talking about miles, they always mean it in hours?

I must have done something wrong in my calculations.

It's neither 10 miles per minute nor 10 miles per hour.

The distance is 10 miles. Upstream it was 10 miles in 15 minutes, i.e. 40 miles per hour. Downstream it was 10 miles in 9 minutes, i.e. 60*10/9 miles per hour. The question is asking us to find how long it would take to travel the river if there were no current at all.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Mon Dec 22, 2008 2:02 am

At full speed, a motorboat can go upstream 10 miles in 15 minutes, and downstream 10 miles in 9 minutes,
at full speed, how long will it take the boat to go 10 miles with no current

Speed = Distance / time

v = speed of boat
u = speed of stream

upstream: 10/( v- u)

downstream 10/ ( v+ u)

v - u 10/15/60

v + u = 10/9/60

solve for v and u

Admission champion, Hauz khaz
011-27565856

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Emawk: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sun Nov 23, 2008 11:21 am

by Emawk » Mon Dec 22, 2008 11:15 pm

Stuart Kovinsky wrote:
Emawk wrote:I did this question using pretty much the same approach as Bret, but I got the wrong answer thinking it was 10miles per minute and not 10miles per hour (since it wasn't mentioned in the question). Or is it common sense that I know that whenever they are talking about miles, they always mean it in hours?

I must have done something wrong in my calculations.
It's neither 10 miles per minute nor 10 miles per hour.

The distance is 10 miles. Upstream it was 10 miles in 15 minutes, i.e. 40 miles per hour. Downstream it was 10 miles in 9 minutes, i.e. 60*10/9 miles per hour. The question is asking us to find how long it would take to travel the river if there were no current at all.

Thanks. I guess I was just seeing things.

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