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

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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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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
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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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rt=.6r(t+24)
4t=144
t=36 minutes
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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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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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Re: Walking at 60% of his usual speed a man takes 24 minutes more to cover [#permalink]
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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
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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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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

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

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

We know, $$Speed ∝\frac{1}{time}$$

60%=3/5
Let, his usual speed be x. If his speed is x, time taken is 1/x, if his speed is 3x/5 then the time taken is 5x/3.

Here, late time~usual time = 24 minute
So, 5x/3~x=25
=>x=36 minute.

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