speed rate question, please help

Question

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.

Brent@GMATPrepNow · Answer

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

cookiemonster26 · Answer

Thanks Brent...

Emawk · Answer

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.

Stuart@KaplanGMAT · Answer

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 · Answer

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

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Emawk · Answer

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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