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A student walks from his house at 2 km/h and reaches school 5 minutes late and if his speed had been 3 km/h he would have reached the school 5 minutes earlier. How far is his school from house?
- a)3 km
- b)2.5 km
- c)2 km
- d)None
- e)All of the above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A student walks from his house at 2 km/h and reaches school 5 minutes ...
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Speed = Distance/Time
Let ideal time taken to reach school is t, distance to school = distance(d)
With a speed of 4km/hr or 4/60 km/min he reaches 5 mins late i.e.
4/60= d/(t+5)
60d = 4t + 20 ----- (1)
Similarly
5/60 = d/(t-10)
60d = 5t - 50 ----- (2)
From eq 1 and 2
4t +20 = 5t - 50
t = 70 mins
60d = 4t + 20 = 280 + 20 = 300
distance(d) = 5 kms
Most Upvoted Answer
A student walks from his house at 2 km/h and reaches school 5 minutes ...
Given:
- The student's speed from his house to school is 2 km/h.
- The student reaches the school 5 minutes late.
- If the student's speed had been 3 km/h, he would have reached the school 5 minutes earlier.
To find:
- The distance between the student's house and the school.
Assumptions:
- The distance between the student's house and school is constant.
Let's solve the problem step by step:
Step 1: Determine the time taken by the student to reach the school at a speed of 2 km/h.
- Let's assume the distance between the house and school is 'd' km.
- The time taken to cover this distance at a speed of 2 km/h is given by the formula: Time = Distance/Speed.
- Therefore, the time taken by the student to reach the school at a speed of 2 km/h is d/2 hours.
Step 2: Determine the time taken by the student to reach the school at a speed of 3 km/h.
- The time taken to cover the same distance at a speed of 3 km/h is given by the formula: Time = Distance/Speed.
- Therefore, the time taken by the student to reach the school at a speed of 3 km/h is d/3 hours.
Step 3: Determine the difference in time between the two scenarios.
- The student reaches the school 5 minutes (or 5/60 hours) late when his speed is 2 km/h.
- The student would have reached the school 5 minutes (or 5/60 hours) earlier if his speed was 3 km/h.
- Therefore, the difference in time between the two scenarios is (d/2 + 5/60) - (d/3 - 5/60) hours.
Step 4: Set up the equation based on the given information.
- We are given that the difference in time between the two scenarios is 5 minutes (or 5/60 hours).
- Therefore, we can write the equation as follows: (d/2 + 5/60) - (d/3 - 5/60) = 5/60.
Step 5: Solve the equation to find the value of 'd'.
- Simplifying the equation, we get: (3d + 5) - (2d - 5) = 5.
- Combining like terms, we get: d + 10 = 5.
- Subtracting 10 from both sides of the equation, we get: d = -5.
Step 6: Interpret the result.
- The negative value for 'd' indicates that the distance between the student's house and school is not possible or undefined.
- Therefore, the correct answer is 'None' (option D) as there is no valid distance that satisfies the given conditions.
Conclusion:
- The distance between the student's house and school cannot be determined based on the information given. Therefore, the correct answer is 'None' (option D).
- The student's speed from his house to school is 2 km/h.
- The student reaches the school 5 minutes late.
- If the student's speed had been 3 km/h, he would have reached the school 5 minutes earlier.
To find:
- The distance between the student's house and the school.
Assumptions:
- The distance between the student's house and school is constant.
Let's solve the problem step by step:
Step 1: Determine the time taken by the student to reach the school at a speed of 2 km/h.
- Let's assume the distance between the house and school is 'd' km.
- The time taken to cover this distance at a speed of 2 km/h is given by the formula: Time = Distance/Speed.
- Therefore, the time taken by the student to reach the school at a speed of 2 km/h is d/2 hours.
Step 2: Determine the time taken by the student to reach the school at a speed of 3 km/h.
- The time taken to cover the same distance at a speed of 3 km/h is given by the formula: Time = Distance/Speed.
- Therefore, the time taken by the student to reach the school at a speed of 3 km/h is d/3 hours.
Step 3: Determine the difference in time between the two scenarios.
- The student reaches the school 5 minutes (or 5/60 hours) late when his speed is 2 km/h.
- The student would have reached the school 5 minutes (or 5/60 hours) earlier if his speed was 3 km/h.
- Therefore, the difference in time between the two scenarios is (d/2 + 5/60) - (d/3 - 5/60) hours.
Step 4: Set up the equation based on the given information.
- We are given that the difference in time between the two scenarios is 5 minutes (or 5/60 hours).
- Therefore, we can write the equation as follows: (d/2 + 5/60) - (d/3 - 5/60) = 5/60.
Step 5: Solve the equation to find the value of 'd'.
- Simplifying the equation, we get: (3d + 5) - (2d - 5) = 5.
- Combining like terms, we get: d + 10 = 5.
- Subtracting 10 from both sides of the equation, we get: d = -5.
Step 6: Interpret the result.
- The negative value for 'd' indicates that the distance between the student's house and school is not possible or undefined.
- Therefore, the correct answer is 'None' (option D) as there is no valid distance that satisfies the given conditions.
Conclusion:
- The distance between the student's house and school cannot be determined based on the information given. Therefore, the correct answer is 'None' (option D).
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