Harold's Time

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sandipgumtya: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sat Jun 07, 2014 5:26 am; Thanked: 3 times

by sandipgumtya » Thu Sep 17, 2015 9:38 pm

Last year Harold's average time to finish the qualifying event was three hours. If he knows that he can increase his speed this year by 20%, how many minutes should it take him to complete the event?
A-150
B-144
C-120
D-90
E-36
I know this is very simple prob.I am getting ans B but OA is A
Help

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Source: Beat The GMAT — Problem Solving | Thu Sep 17, 2015 9:38 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Fri Sep 18, 2015 2:18 am

sandipgumtya wrote:Last year Harold's average time to finish the qualifying event was three hours. If he knows that he can increase his speed this year by 20%, how many minutes should it take him to complete the event?
A-150
B-144
C-120
D-90
E-36
I know this is very simple prob.I am getting ans B but OA is A
Help

The distance before and after will be the same.
speed = distance/time
distance = speed x time

therefore speed before x time before = new speed x new time
S X T = 1.2S X T/1.2

T/1.2 = 180/1.2 = 1800/12 = 150

ANS= A

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 18, 2015 3:26 am

sandipgumtya wrote:Last year Harold's average time to finish the qualifying event was three hours. If he knows that he can increase his speed this year by 20%, how many minutes should it take him to complete the event?
A-150
B-144
C-120
D-90
E-36

20% faster = 120% of last year's speed = 6/5 of last year's speed.
Rate and time are RECIPROCALS.
6/5 of last year's speed implies 5/6 of last year's time:
(5/6)(3 hours) = (5/6)(180 minutes) = 150 minutes.

The correct answer is A.

Alternate approach:
Let last year's speed = 10 feet per minute.
Since last year Harold traveled at a speed of 10 feet per minute for 180 minutes, the total distance = rt = 10*180 = 1800 feet.
If the speed is increased by 20% to 12 feet per minute, the time to travel 1800 feet = d/r = 1800/12 = 150 minutes.

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Bullzi: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Thu May 28, 2015 1:13 am; Thanked: 5 times

by Bullzi » Fri Sep 18, 2015 3:37 am

Hello..

My approach,

1. rate x time = distance
2. Convert 3 hours to 180 mins as all answer options are minutes
3. LY - r x 180 = d
4. TY - (120/100)r x t = d
5. Solve #4 after substituting value of d from #3
6. (12/10)t = 180 --> t = 150

Bullzi

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sandipgumtya: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sat Jun 07, 2014 5:26 am; Thanked: 3 times

by sandipgumtya » Fri Sep 18, 2015 5:40 am

Hello Mitch,
20% reduction of 3 hr equals 144 mins.Isn't it?Where am i going wrong?

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Sep 18, 2015 9:19 am

Hi sandipgumtya,

We're told that the SPEED is 20% faster; with your math, you're attempting to manipulate the TIME, which is why that result is incorrect.

GMAT assassins aren't born, they're made,
Rich

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sandipgumtya: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sat Jun 07, 2014 5:26 am; Thanked: 3 times

by sandipgumtya » Fri Sep 18, 2015 9:29 am

As speed and time are inversely proportional,20% faster means 20% lesser time.Is this concept wrong. Pl correct me in detail.

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by [email protected] » Fri Sep 18, 2015 9:51 am

Hi sandipgymtya,

Percent Change is calculated based on the ORIGINAL numbers involved. While speed and time ARE related, their respective percent changes are NOT the same.

Assuming that the distance stays the same, Increasing a speed by 20% decreases the time by 16 1/6% (not 20%).

Here's why:

Original speed and time:
D = (R)(T)

20% increase in speed:
D = (6/5)(R)(5/6)(T)

Since the distance is the same, the (6/5) is 'cancelled out' by the (5/6) - the speed increased by 1/5 (or 20%), but the time decreased by 1/6 (or 16 1/6%).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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sandipgumtya: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sat Jun 07, 2014 5:26 am; Thanked: 3 times

by sandipgumtya » Fri Sep 18, 2015 10:43 am

thanks Rich for this nice explanation.got it clear now.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 18, 2015 1:04 pm

sandipgumtya wrote:As speed and time are inversely proportional,20% faster means 20% lesser time.Is this concept wrong. Pl correct me in detail.

As noted above:

20% faster = (120/100)r = (6/5)r.
Since rate and time are reciprocals:
(6/5)r --> (5/6)t --> 1/6 less time.

Other examples:

50% faster = (150/100)r = (3/2)r.
Since rate and time are reciprocals:
(3/2)r --> (2/3)t --> 1/3 less time.

20% slower = (80/100)r = (4/5)r.
Since rate and time are reciprocals:
(4/5)r --> (5/4)t = 1/4 more time.

50% slower = (50/100)r = (1/2)r.
Since rate and time are reciprocals:
(1/2)r --> 2t --> twice the time.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

hi

by Jeff@TargetTestPrep » Mon Dec 11, 2017 10:46 am

sandipgumtya wrote:Last year Harold's average time to finish the qualifying event was three hours. If he knows that he can increase his speed this year by 20%, how many minutes should it take him to complete the event?
A-150
B-144
C-120
D-90
E-36

Recall that rate x time = job (or rate = job/time, or time = job/rate). Since Harold's time to complete the event was 3 hours, we can say that his rate was 1 job per 3 hours; i.e., his rate is 1/3. Since he's increasing his speed by 20%, his new rate is:

(1/3) x 1.2

(1/3) x 12/10 = 4/10 = 2/5

Since his new rate is 2/5, his new time is 1/(2/5) = 5/2 = 2.5 hours. Thus he can complete the event in 2.5 x 60 = 150 minutes.

Answer: A

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