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Amita travels from her house at 3(1/2)km/h and reaches her school 6 minutes tale. The next day she travels at 4(1/2)km/h and reaches her school 10 minutes early. What is the distance between her house and the school.
- a)4.2 km
- b)5.4 km
- c)5.6 km
- d)4.8 km
- e)None of the above/More than one of the above
Correct answer is option 'A'. Can you explain this answer?
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Amita travels from her house at 3(1/2)km/hand reaches her school 6 min...
To find the distance between Amita's house and her school, we can use the formula:
Distance = Speed x Time
Let's break down the given information and solve the problem step by step:
1. Amita's speed on the first day: 3(1/2) km/h
Amita reaches her school 6 minutes late.
2. Amita's speed on the second day: 4(1/2) km/h
Amita reaches her school 10 minutes early.
To calculate the distance, we need to find the time taken on both days.
Calculating Time Taken:
1. On the first day:
Amita reaches her school 6 minutes late.
So, the time taken on the first day = Time taken - 6 minutes
2. On the second day:
Amita reaches her school 10 minutes early.
So, the time taken on the second day = Time taken + 10 minutes
Now, let's calculate the time taken on both days:
3. Time taken on the first day:
Let's assume it to be T1.
T1 - 6 minutes = Time taken to reach the school at a speed of 3(1/2) km/h
4. Time taken on the second day:
Let's assume it to be T2.
T2 + 10 minutes = Time taken to reach the school at a speed of 4(1/2) km/h
Calculating Distance:
5. Distance on the first day:
Distance = Speed x Time
Distance = 3(1/2) km/h x T1
6. Distance on the second day:
Distance = 4(1/2) km/h x T2
Now, let's solve the equations to find the values of T1 and T2:
7. From equation 3:
T1 - 6 minutes = Distance / 3(1/2) km/h
8. From equation 4:
T2 + 10 minutes = Distance / 4(1/2) km/h
Since the distance traveled on both days is the same, we can equate the two equations:
9. T1 - 6 minutes = T2 + 10 minutes
Now, let's solve for T1 and T2:
10. T1 = T2 + 16 minutes
Substituting the value of T1 in equation 7:
11. T2 + 16 minutes - 6 minutes = Distance / 3(1/2) km/h
Simplifying:
12. T2 + 10 minutes = Distance / 3(1/2) km/h
Substituting the value of T2 in equation 8:
13. T2 + 10 minutes + 10 minutes = Distance / 4(1/2) km/h
Simplifying:
14. T2 + 20 minutes = Distance / 4(1/2) km/h
Now, equating equations 12 and 14:
15. Distance / 3(1/2) km/h = Distance / 4(1/2) km/h
Cross-multiplying:
16. 4(1/2) * Distance = 3(1/2) * Distance
Simplifying:
17. Distance = Distance
Therefore, the distance traveled on both
Distance = Speed x Time
Let's break down the given information and solve the problem step by step:
1. Amita's speed on the first day: 3(1/2) km/h
Amita reaches her school 6 minutes late.
2. Amita's speed on the second day: 4(1/2) km/h
Amita reaches her school 10 minutes early.
To calculate the distance, we need to find the time taken on both days.
Calculating Time Taken:
1. On the first day:
Amita reaches her school 6 minutes late.
So, the time taken on the first day = Time taken - 6 minutes
2. On the second day:
Amita reaches her school 10 minutes early.
So, the time taken on the second day = Time taken + 10 minutes
Now, let's calculate the time taken on both days:
3. Time taken on the first day:
Let's assume it to be T1.
T1 - 6 minutes = Time taken to reach the school at a speed of 3(1/2) km/h
4. Time taken on the second day:
Let's assume it to be T2.
T2 + 10 minutes = Time taken to reach the school at a speed of 4(1/2) km/h
Calculating Distance:
5. Distance on the first day:
Distance = Speed x Time
Distance = 3(1/2) km/h x T1
6. Distance on the second day:
Distance = 4(1/2) km/h x T2
Now, let's solve the equations to find the values of T1 and T2:
7. From equation 3:
T1 - 6 minutes = Distance / 3(1/2) km/h
8. From equation 4:
T2 + 10 minutes = Distance / 4(1/2) km/h
Since the distance traveled on both days is the same, we can equate the two equations:
9. T1 - 6 minutes = T2 + 10 minutes
Now, let's solve for T1 and T2:
10. T1 = T2 + 16 minutes
Substituting the value of T1 in equation 7:
11. T2 + 16 minutes - 6 minutes = Distance / 3(1/2) km/h
Simplifying:
12. T2 + 10 minutes = Distance / 3(1/2) km/h
Substituting the value of T2 in equation 8:
13. T2 + 10 minutes + 10 minutes = Distance / 4(1/2) km/h
Simplifying:
14. T2 + 20 minutes = Distance / 4(1/2) km/h
Now, equating equations 12 and 14:
15. Distance / 3(1/2) km/h = Distance / 4(1/2) km/h
Cross-multiplying:
16. 4(1/2) * Distance = 3(1/2) * Distance
Simplifying:
17. Distance = Distance
Therefore, the distance traveled on both
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Amita travels from her house at 3(1/2)km/hand reaches her school 6 minutes tale. The next day she travels at 4(1/2)km/hand reaches her school 10 minutes early. What is the distance between her house and the school.a)4.2kmb)5.4 kmc)5.6 kmd)4.8 kme)None of the above/More than one of the aboveCorrect answer is option 'A'. Can you explain this answer?
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