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In a specific river

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by gmatdriller » Wed May 30, 2012 12:10 am
In a specific river, the current is 6 miles per hour. A riverboat, which has a top speed of 18 miles per hour in still waters, makes daily round trips up the river. How far upstream (against the current) does the riverboat transport passengers if the boat travels at its top speed the entire time, and the round trip upstream and back takes 10 hours?

A: 54 miles B: 60 miles C: 72 miles D: 80 miles E: 90 miles

pls someone explain the question, possibly with diagrams...

Thanks. OAD
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by Anurag@Gurome » Wed May 30, 2012 12:32 am
gmatdriller wrote:In a specific river, the current is 6 miles per hour. A riverboat, which has a top speed of 18 miles per hour in still waters, makes daily round trips up the river. How far upstream (against the current) does the riverboat transport passengers if the boat travels at its top speed the entire time, and the round trip upstream and back takes 10 hours?
Top speed of the boat in still water = 18 mph
Top speed of the boat in downstream (along the current) = (18 + 6) mph = 24 mph
Top speed of the boat in upstream (against the current) = (18 - 6) mph = 12 mph

Let us assume the boat transport passengers d miles upstream.
As the boat makes round trips, the boat also travels d miles downstream.
Hence, the boat covers a total round strip distance of 2d miles in 10 hours.

--> 10 hours = Time taken to cover d miles in upstream + Time taken to cover d miles in downstream
--> 10 = d/12 + d/24
--> 10 = 3d/24 = d/8
--> d = 80

Hence, correct answer is D.
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by mdavidm_531 » Wed May 30, 2012 12:44 am
gmatdriller wrote:In a specific river, the current is 6 miles per hour. A riverboat, which has a top speed of 18 miles per hour in still waters, makes daily round trips up the river. How far upstream (against the current) does the riverboat transport passengers if the boat travels at its top speed the entire time, and the round trip upstream and back takes 10 hours?

A: 54 miles B: 60 miles C: 72 miles D: 80 miles E: 90 miles

pls someone explain the question, possibly with diagrams...

Thanks. OAD
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by GMATGuruNY » Wed May 30, 2012 2:33 am
gmatdriller wrote:In a specific river, the current is 6 miles per hour. A riverboat, which has a top speed of 18 miles per hour in still waters, makes daily round trips up the river. How far upstream (against the current) does the riverboat transport passengers if the boat travels at its top speed the entire time, and the round trip upstream and back takes 10 hours?

A: 54 miles B: 60 miles C: 72 miles D: 80 miles E: 90 miles

pls someone explain the question, possibly with diagrams...

Thanks. OAD
The rate upstream = boat rate - current rate = 18-6 = 12 miles per hour.
The rate downstream = boat rate + current rate = 18+6 = 24 miles per hour.

We can plug in the answers, which represent the distance in each direction.

Answer choice C: 72 miles
Time upstream + time downstream = 72/12 + 72/24 = 9 hours.
Since the total time must be just a bit longer -- 10 hours -- the distance must be just a bit greater.

The correct answer is D.
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by gmatdriller » Thu May 31, 2012 4:14 am
Thanks for all your wonderful contributions.

Meanwhile, the diagrams by mdavidm made quicker clarifications. Further,
I appreciate the intuitive part added by Anurag; also, GMATGuru has been
a great inspiration on this forum.
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by GMAT Kolaveri » Thu May 31, 2012 8:17 am
Awesome explanations by GMATGuruNY, Anurag and mdavidm.

Anurag's explanation reminds me of good old school days when the Math teacher used to award marks for just writing down what is given in the question :)

Mitch always stresses on "looking at AO before solving"
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