Walking at 60% of his usual speed a man takes 24 minutes more to cover : Problem Solving (PS)

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Walking at 60% of his usual speed a man takes 24 minutes more to cover

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Math Expert

Joined: 02 Sep 2009

Posts: 52437

Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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08 Dec 2015, 02:06

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Difficulty:

25% (medium)

Question Stats:

79% (02:04) correct

21% (02:53) wrong

based on 156 sessions

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Walking at 60% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?

A. 30
B. 36
C. 42
D. 48
E. 54

Spoiler: OA

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Re: Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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08 Dec 2015, 02:15

speed is inversly proprtional to time

walking at 60% of speed meand 3/5s takes 5/3t.
It takes 24 minutes extra to cover the distance. then

5/3t=t+24

5t=3t+72

2t=72

t=36.

Option B is correct

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Re: Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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08 Dec 2015, 02:17

walking at 60% of his usual speed =3/5
since speed is inversely proportional to time
time taken =5/3
now 5/3 =(1+2/3)
an increase of 2/3=24 minutes
therefore usual time =24*3/2=36 minutes

Joined: 07 Dec 2014

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Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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08 Dec 2015, 15:40

rt=.6r(t+24)
4t=144
t=36 minutes

Manager

Joined: 14 May 2015

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Re: Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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07 May 2017, 02:41

time is inverse to speed
60% reduce speed= (100-60) or 40% more time
40%=24
100%=60
usual time=60-24=36

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Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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08 May 2017, 05:47

Bunuel wrote:

Walking at 60% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?

A. 30
B. 36
C. 42
D. 48
E. 54

Another way: To use r*t=D with just one variable, choose a number that's easily multiplied by .6 for normal rate

1. Let 10 (mi per min) be his normal rate
Slower rate is 60% of 10 = 6 (mi per min)

2. Let x be normal time, and (x+24) be longer time.

3. r*t = D

Normal: 10*x = D
Slower: 6*(x+24) = D

4.Ds are equal, so

10x = 6x+144
4x=144, so
x = 36
Answer B
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Re: Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]

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03 Apr 2018, 09:23

Top Contributor

Bunuel wrote:

Walking at 60% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?

A. 30
B. 36
C. 42
D. 48
E. 54

Let's start with a WORD EQUATION:
distance traveled at REGULAR speed = distance traveled at REDUCED speed

distance = (rate)(time)
Let R = REGULAR speed
So 0.6R = REDUCED speed
Let t = travel time (in minutes) at REGULAR speed
So t + 24 = travel time (in minutes) at REDUCED speed

Now plug this information into our WORD EQUATION to get:
Rt = (0.6R)(t + 24)
Divide both sides by R to get: t = (0.6)(t + 24)
Rewrite 0.6 as 3/5 to get: t = (3/5)(t + 24)
Expand: t = 3t/5 + 72/5
Multiply both sides by 5 to get: 5t = 3t + 72
Solve to get: t = 36

Answer: B

Cheers,
Brent
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