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

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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

by VJesus12 » Wed Jun 02, 2021 10:50 am

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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

Source: GMAT Club Tests

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### Re: Walking at $$60\%$$ of his usual speed a man takes $$24$$ minutes more to cover a distance. What is his usual time t

by [email protected] » Thu Jun 03, 2021 5:01 am
VJesus12 wrote:
Wed Jun 02, 2021 10:50 am
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

Source: GMAT Club Tests
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

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### Re: Walking at $$60\%$$ of his usual speed a man takes $$24$$ minutes more to cover a distance. What is his usual time t

by swerve » Fri Jun 04, 2021 6:44 am
VJesus12 wrote:
Wed Jun 02, 2021 10:50 am
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

Walking at 60% of speed means $$\dfrac{3}{5}s$$ takes $$\dfrac{5}{3}t.$$
It takes $$24$$ minutes extra to cover the distance. Then
$$\dfrac{5}{3}t=t+24$$
$$5t=3t+72$$
$$2t=72$$
$$t=36.$$