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If a man reduces his speed to 2/3 , he takes 1 hr more in walking a certain distance. The time (in hr) to cover the distance with his normal speed is
- a)1
- b)2
- c)3
- d)1.5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If a man reduces his speed to 2/3 , he takes 1 hr more in walking a ce...
Suppose man covers x km in y hours
His normal speed = x/y km/hr
Reduced speed = 2x/3x km/hr
Time taken to cover x km = x/2x/3y hrs = 3y/2 hrs
By hypothesis
3/2 y = y + 1
or y = 2 hrs
His normal speed = x/y km/hr
Reduced speed = 2x/3x km/hr
Time taken to cover x km = x/2x/3y hrs = 3y/2 hrs
By hypothesis
3/2 y = y + 1
or y = 2 hrs
Most Upvoted Answer
If a man reduces his speed to 2/3 , he takes 1 hr more in walking a ce...
Understanding the problem:
The problem states that a man reduces his speed to 2/3 of his normal speed, and as a result, he takes 1 hour more to walk a certain distance. We need to determine the time it takes for the man to cover the same distance with his normal speed.
Solution:
Let's assume the man's normal speed is 's' units of distance per hour, and the distance he needs to cover is 'd' units.
Step 1: Determine the time taken at reduced speed:
When the man reduces his speed to 2/3, his new speed becomes (2/3)s units of distance per hour. Let's denote the time taken to cover the distance at this reduced speed as 't'.
We can calculate 't' using the formula:
Distance = Speed x Time
d = (2/3)s x t
Simplifying the equation, we get:
t = (3/2)(d/s)
Step 2: Determine the time taken at normal speed:
We are given that when the man reduces his speed, he takes 1 hour more to cover the distance. Therefore, the time taken at normal speed will be 't + 1' hours.
Step 3: Equate the time taken at normal speed:
Using the information from step 1 and step 2, we can set up the equation:
t + 1 = (3/2)(d/s)
Step 4: Solve the equation:
To solve the equation, we need to isolate 't':
t = (3/2)(d/s) - 1
t = (3d - 2s)/ (2s)
Step 5: Determine the time taken at normal speed:
From the equation in step 4, we can see that the time taken at normal speed is (3d - 2s)/(2s) hours.
Therefore, the correct answer is option 'B' - 2 hours.
The problem states that a man reduces his speed to 2/3 of his normal speed, and as a result, he takes 1 hour more to walk a certain distance. We need to determine the time it takes for the man to cover the same distance with his normal speed.
Solution:
Let's assume the man's normal speed is 's' units of distance per hour, and the distance he needs to cover is 'd' units.
Step 1: Determine the time taken at reduced speed:
When the man reduces his speed to 2/3, his new speed becomes (2/3)s units of distance per hour. Let's denote the time taken to cover the distance at this reduced speed as 't'.
We can calculate 't' using the formula:
Distance = Speed x Time
d = (2/3)s x t
Simplifying the equation, we get:
t = (3/2)(d/s)
Step 2: Determine the time taken at normal speed:
We are given that when the man reduces his speed, he takes 1 hour more to cover the distance. Therefore, the time taken at normal speed will be 't + 1' hours.
Step 3: Equate the time taken at normal speed:
Using the information from step 1 and step 2, we can set up the equation:
t + 1 = (3/2)(d/s)
Step 4: Solve the equation:
To solve the equation, we need to isolate 't':
t = (3/2)(d/s) - 1
t = (3d - 2s)/ (2s)
Step 5: Determine the time taken at normal speed:
From the equation in step 4, we can see that the time taken at normal speed is (3d - 2s)/(2s) hours.
Therefore, the correct answer is option 'B' - 2 hours.
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If a man reduces his speed to 2/3 , he takes 1 hr more in walking a certain distance. The time (in hr) to cover the distance with his normal speed isa)1b)2c)3d)1.5Correct answer is option 'B'. Can you explain this answer?
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