A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?
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2 hours 30 minutes
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2 hours 20 minutes
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3 hours 20 minutes
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3 hours 30 minutes
Let usual time be T. At 5/6 rate, time taken is T/(5/6) = 6T/5. The difference is 6T/5 - T = T/5 = 40 minutes, so T = 200 minutes = 3 hours 20 minutes. This represents the normal travel time at full speed.
To solve this problem, let's assume the person's usual time is represented by "x" minutes.
According to the given information, the person is walking at 5/6 of his usual rate. This means he is walking at a speed of (5/6)x minutes per minute.
We are also given that the person is 40 minutes late. This means the actual time taken by the person is (x + 40) minutes.
We can set up an equation based on the given information:
(x + 40) = (5/6)x
To solve for x, we can multiply both sides of the equation by 6 to eliminate the fraction:
6(x + 40) = 5x
Expanding the equation:
6x + 240 = 5x
Now, we can subtract 5x from both sides:
x + 240 = 0
x = -240
Since time cannot be negative, we can discard the negative solution.
Therefore, the person's usual time is 240 minutes, which is equivalent to 4 hours.
Converting 240 minutes to hours and minutes:
240 minutes = 4 hours
So, the person's usual time is 4 hours.
The correct answer is C) 3 hours 20 minutes.