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# Speed Problem 4

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Intern
Joined: 17 Apr 2010
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Speed Problem 4 [#permalink]  25 Apr 2010, 11:53
00:00

Difficulty:

(N/A)

Question Stats:

100% (05:14) correct 0% (00:00) wrong based on 1 sessions
Hi everybody.

A boat travels up the river and down the river the same distance. If the average relative speed of the boat 48 mph and the speed of the river is 10 mph, what is the upriver speed of the boat?

My solution:
Up stream the boat must be 10 mph slower than average. So I came up with 38 mph.

However, the correct answer is: 40 mph.

Can anybody explain?
_________________

Consider giving kudos, if you like my thread!

FYI: Questions are from the workbook of my prep course.

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
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Kudos [?]: 1338 [2] , given: 235

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 12:02
2
KUDOS
gmatt14 wrote:
Hi everybody.

A boat travels up the river and down the river the same distance. If the average relative speed of the boat 48 mph and the speed of the river is 10 mph, what is the upriver speed of the boat?

My solution:
Up stream the boat must be 10 mph slower than average. So I came up with 38 mph.

However, the correct answer is: 40 mph.

Can anybody explain?

40 is correct, average speed = total Distance/total Time

Let speed of boat = $$x$$
upstream speed = $$x-10$$
downstream speed = $$x+10$$

total distance covered = $$2y$$
time taken upwards = $$\frac{y}{{x-10}}$$
time taken downwards =$$\frac{y}{{x+10}}$$

total time = $$\frac{y}{{x-10}} + \frac{y}{{x+10}}$$

average speed = $$\frac{2y}{{{y/(x-10)}+ y/(x+10)}} = \frac{{x^2-100}}{x}= 48$$

=> $$x^2 - 48x - 100 = 0$$
= $$(x-50)(x+2) = 0$$, x cannot be -ve thus$$x=50$$

upstream speed =$$x-10 = 50-10 = 40$$

PS: 48 is the average relative speed.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

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Intern
Joined: 17 Apr 2010
Posts: 38
Followers: 1

Kudos [?]: 3 [0], given: 25

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 12:44
Took me some time, but I figured out your approach. I got stuck at your average speed equation.

Although I understand it now, I don't know wheather I could have done it on the GMAT in 2 min.
Is there a simpler way???????
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Consider giving kudos, if you like my thread!

FYI: Questions are from the workbook of my prep course.

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
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Kudos [?]: 1338 [1] , given: 235

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 12:48
1
KUDOS
It can be done in 2 min if you understood the concept. Otherwise we could have used POE on the answer choices.

You can remember this result

if a and b are two speeds for same distance( say x) traveled then the average speed for 2x is 2ab/(a+b)

this way you can put a = x-10 , b = x+10 and 2ab/(a+b) = 48
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Joined: 17 Apr 2010
Posts: 38
Followers: 1

Kudos [?]: 3 [0], given: 25

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 13:10
Ok. I can follow you. However, I have difficulties internalizing it.
Can you recommend a source where I could review this topic?
_________________

Consider giving kudos, if you like my thread!

FYI: Questions are from the workbook of my prep course.

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 208

Kudos [?]: 1338 [1] , given: 235

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 13:26
1
KUDOS
gmatt14 wrote:
Ok. I can follow you. However, I have difficulties internalizing it.
Can you recommend a source where I could review this topic?

You can buy Manhattan guides which are very good though I have not done for maths( Followed Manhattan SC only).
with every book you will get good question bank and 6 Cats( CATs are common for all and bank is book specific)

Also be regular in math forums and do read GMAT CLUB math book.
gmat-math-book-87417.html

PS: Manhattan Word translation might cover the above topic. Its number property book is also very nice.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Joined: 17 Apr 2010
Posts: 38
Followers: 1

Kudos [?]: 3 [0], given: 25

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 13:48
_________________

Consider giving kudos, if you like my thread!

FYI: Questions are from the workbook of my prep course.

Manager
Joined: 27 Feb 2010
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Re: Speed Problem 4 [#permalink]  25 Apr 2010, 18:29
gurpreetsingh +1kudos for you. Thanks, your solution helped me too. I see that you have been actively participating in the forum since few months, when are you planning for the actual exam? are you still a student?
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 208

Kudos [?]: 1338 [0], given: 235

Re: Speed Problem 4 [#permalink]  25 Apr 2010, 21:07
zz0vlb wrote:
gurpreetsingh +1kudos for you. Thanks, your solution helped me too. I see that you have been actively participating in the forum since few months, when are you planning for the actual exam? are you still a student?

Yes I m still preparing for the GMAT, actually I need a lot of improvement in my Verbal. I can not think of giving the exam without improving verbal.

I believe we should give the exam only when we are well prepared. Once prepared any one can beat this exam.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Joined: 20 Nov 2009
Posts: 167
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Re: Speed Problem 4 [#permalink]  26 Apr 2010, 03:17
Gurpreet, thanks for your explanation! +1
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Senior Manager
Joined: 12 Jan 2010
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Re: Speed Problem 4 [#permalink]  26 Apr 2010, 07:06
Hi,

Just an alternate solution to get the answer faster. Gurpreet's answer explains the problem step by step, this is just a formula that can get you straight to the equation.

Since the distance traveled both upstream and downstream is same we can use the average speed formula

Average speed = 2xy/x + y
Let assume speed of boat = s
Speed of stream
Speed upstream = x = s-10
Speed downstream = y = s+10
Average speed = 48

Plug in the values we get
2*(s-10)(s+10)/s-10+s+10 = 48

s^2-100/s = 48
s^2-100 - 48s = 0

s = 50 or -2

So speed upstream = s-10 = 50-10 = 40 mi/hr
_________________

Run towards the things that make you uncomfortable daily. The greatest risk is not taking risks
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Re: Speed Problem 4   [#permalink] 26 Apr 2010, 07:06
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