if Arvind cycles 10km/hr ,he reaches the school late by 4min,/if he cycles 12km/hr,he reaches the school early by 2min,find the distance of the school from his home.
Let's assume that the distance from Arvind's home to the school is 'd' kilometers.
According to the first statement, when Arvind cycles at 10 km/hr, he reaches the school late by 4 minutes. This means that the time taken to reach the school at this speed is greater than the expected time.
Using the formula: time = distance / speed, we can write the equation as:
d / 10 = t + 4
According to the second statement, when Arvind cycles at 12 km/hr, he reaches the school early by 2 minutes. This means that the time taken to reach the school at this speed is less than the expected time.
Using the same formula, we can write another equation as:
d / 12 = t - 2
To find the distance, we need to solve these two equations simultaneously.
Simplifying the equations:
1) d = 10t + 40
2) d = 12t - 24
Setting the two expressions for 'd' equal to each other:
10t + 40 = 12t - 24
Rearranging the equation to isolate 't':
40 + 24 = 12t - 10t
64 = 2t
t = 32 minutes
Substituting the value of 't' back into one of the original equations:
d = 12t - 24
d = (12 * 32) - 24
d = 384 - 24
d = 360 kilometers
Therefore, the distance of the school from Arvind's home is 360 kilometers.
To find the distance of the school from Arvind's home, we can use the concept of average speed. Average speed is given by the formula:
Average Speed = Total Distance / Total Time
Let's assume the distance from Arvind's home to the school is 'd' km.
According to the first part of the question:
Arvind cycles at a speed of 10 km/hr and reaches the school late by 4 minutes. So, we need to consider the time taken as (t + 4) minutes to cover the distance 'd' km. Here, we convert 4 minutes to hours by dividing it by 60.
Therefore, the time taken in hours can be represented as (t + 4)/60 hours.
According to the second part of the question:
Arvind cycles at a speed of 12 km/hr and reaches the school early by 2 minutes. So, we need to consider the time taken as (t - 2) minutes to cover the same distance 'd' km. Here, we convert 2 minutes to hours by dividing it by 60.
Therefore, the time taken in hours can be represented as (t - 2)/60 hours.
Now, let's use the average speed formula for both scenarios:
For the first scenario:
Average speed = 10 km/hr
Total distance = d km
Total time = (t + 4)/60 hours
Using the formula:
10 = d / [(t + 4) / 60]
For the second scenario:
Average speed = 12 km/hr
Total distance = d km
Total time = (t - 2)/60 hours
Using the formula:
12 = d / [(t - 2) / 60]
Now, we have two equations:
10 = d / [(t + 4) / 60]
12 = d / [(t - 2) / 60]
We can solve these equations together to find the values of 'd' and 't'. After obtaining the values, we can find the actual distance of the school from Arvind's home.