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Walking at 3/4 of his usual speed ,a man is late by 2 1/2 hr. the usual time is
- a)7
- b)7 1/2
- c)8 1/2
- d)8
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Walking at 3/4 of his usual speed ,a man is late by 2 1/2 hr. the usua...
Most Upvoted Answer
Walking at 3/4 of his usual speed ,a man is late by 2 1/2 hr. the usua...
Usual speed = S Usual time = T Distance = D New Speed is 3/4 S New time is 4/3 T 4/3 T, T = 5/2 T=15/2 = 7 1/2
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Walking at 3/4 of his usual speed ,a man is late by 2 1/2 hr. the usua...
Given information:
- The man is walking at 3/4 of his usual speed.
- He is late by 2 1/2 hours.
To find:
The usual time it takes for the man to reach his destination.
Let's assume the man's usual speed is S and the usual time taken is T.
Calculating the time taken when walking at 3/4 of the usual speed:
New speed = 3/4 * S
New time = T + 2 1/2
Step 1: Convert 2 1/2 hours to improper fraction
2 1/2 = 5/2
Step 2: Write the equation using the given information
T + 5/2 = (3/4)S
Step 3: Solve the equation for S
Multiply both sides of the equation by 4 to eliminate the fraction:
4T + 10/2 = 3S
4T + 5 = 3S
Now, let's consider option (a) 7 hours as the usual time.
Step 4: Substitute the value of T into the equation
4(7) + 5 = 3S
28 + 5 = 3S
33 = 3S
Since 33 is not divisible by 3, option (a) is not the correct answer.
Step 5: Repeat steps 4 and 5 for options (b), (c), and (d)
(b) 7 1/2 hours as the usual time:
4(7 1/2) + 5 = 3S
30 + 5 = 3S
35 = 3S
35 is not divisible by 3, so option (b) is not the correct answer.
(c) 8 1/2 hours as the usual time:
4(8 1/2) + 5 = 3S
34 + 5 = 3S
39 = 3S
39 is divisible by 3, so option (c) could be the correct answer.
(d) 8 hours as the usual time:
4(8) + 5 = 3S
32 + 5 = 3S
37 = 3S
37 is not divisible by 3, so option (d) is not the correct answer.
Therefore, the correct answer is option (c) 8 1/2 hours.
- The man is walking at 3/4 of his usual speed.
- He is late by 2 1/2 hours.
To find:
The usual time it takes for the man to reach his destination.
Let's assume the man's usual speed is S and the usual time taken is T.
Calculating the time taken when walking at 3/4 of the usual speed:
New speed = 3/4 * S
New time = T + 2 1/2
Step 1: Convert 2 1/2 hours to improper fraction
2 1/2 = 5/2
Step 2: Write the equation using the given information
T + 5/2 = (3/4)S
Step 3: Solve the equation for S
Multiply both sides of the equation by 4 to eliminate the fraction:
4T + 10/2 = 3S
4T + 5 = 3S
Now, let's consider option (a) 7 hours as the usual time.
Step 4: Substitute the value of T into the equation
4(7) + 5 = 3S
28 + 5 = 3S
33 = 3S
Since 33 is not divisible by 3, option (a) is not the correct answer.
Step 5: Repeat steps 4 and 5 for options (b), (c), and (d)
(b) 7 1/2 hours as the usual time:
4(7 1/2) + 5 = 3S
30 + 5 = 3S
35 = 3S
35 is not divisible by 3, so option (b) is not the correct answer.
(c) 8 1/2 hours as the usual time:
4(8 1/2) + 5 = 3S
34 + 5 = 3S
39 = 3S
39 is divisible by 3, so option (c) could be the correct answer.
(d) 8 hours as the usual time:
4(8) + 5 = 3S
32 + 5 = 3S
37 = 3S
37 is not divisible by 3, so option (d) is not the correct answer.
Therefore, the correct answer is option (c) 8 1/2 hours.
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