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By walking at 3/4 of his usual speed, a man reaches office 20 min later than usual. His usual time is ?
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Most Upvoted Answer
By walking at 3/4 of his usual speed, a man reaches office 20 min late...
Let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+20
4T=3T+60...therefor T=60min
usual speed and time let say s,t
st=3/4s(t+20)
4st=3st+15s
t=15
so Ans = 15MIN.
Community Answer
By walking at 3/4 of his usual speed, a man reaches office 20 min late...
Given:
- The man reaches office 20 minutes later than usual.
- The man walks at 3/4 of his usual speed.

To find:
- The man's usual time.

Assumptions:
- The distance between the man's home and office remains constant.

Solution:
Let's assume the man's usual time to reach the office is "t" minutes.

Time taken when walking at 3/4 of his usual speed:
- When the man walks at 3/4 of his usual speed, he covers 3/4 of the distance in the same time "t" minutes.
- Therefore, the time taken to cover 3/4 of the distance at 3/4 of his usual speed is (3/4)t minutes.

Time taken to cover the remaining 1/4 of the distance:
- As the man is walking at 3/4 of his usual speed, it will take him longer to cover the remaining 1/4 of the distance.
- Let's assume the time taken to cover the remaining 1/4 of the distance is "x" minutes.

Total time taken:
- The total time taken to reach the office when walking at 3/4 of his usual speed is (3/4)t + x minutes.

Given:
- The man reaches the office 20 minutes later than usual.
- Therefore, the total time taken when walking at 3/4 of his usual speed is t + 20 minutes.

Equation:
- We can equate the two expressions for the total time taken:
(3/4)t + x = t + 20

Solving the equation:
- Let's solve the equation to find the value of "t", which represents the man's usual time.

Step 1:
- Simplify the equation by multiplying both sides by 4 to eliminate the fraction:
4(3/4)t + 4x = 4(t + 20)
3t + 4x = 4t + 80

Step 2:
- Rearrange the equation to isolate the variable "t":
4x - 80 = 4t - 3t
x - 20 = t

Conclusion:
- The man's usual time, represented by "t", is equal to the time taken to cover the remaining 1/4 of the distance, which is denoted by "x".
- Therefore, the man's usual time to reach the office is 20 minutes.
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