Alka walks at the speed of 5 kmph but find that she is late to school by 7 minutes. However next day she walks at the speed of 6 kmph, and reaches school 5 minutes earlear than the usual time. Calculate the distance covered to reach the school.
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To calculate the distance covered by Alka to reach the school, we need to analyze the time differences between the two scenarios.
Let's assume the usual time it takes Alka to reach school is "t" hours.
1. In the first scenario:
At a speed of 5 kmph, Alka is late by 7 minutes. So, the time taken to reach the school is "t + 7 minutes" or "t + 7/60 hours".
2. In the second scenario:
At a speed of 6 kmph, Alka reaches 5 minutes earlier than usual. So, the time taken to reach school is "t - 5 minutes" or "t - 5/60 hours".
Now, we can use the formula:
Distance = Speed * Time
In the first scenario, distance = 5 kmph * (t + 7/60) hours
In the second scenario, distance = 6 kmph * (t - 5/60) hours
Since the distance covered is the same in both scenarios, we can set these two expressions equal to each other and solve for "t" to find the distance.
5(t + 7/60) = 6(t - 5/60)
Simplifying the equation:
5t + 35/60 = 6t - 5/60
Multiplying both sides by 60 to eliminate the fractions:
300t + 35 = 360t - 5
Grouping the "t" terms and the constant terms:
300t - 360t = -5 - 35
-60t = -40
Dividing both sides by -60:
t = 2/3 hours
Finally, we can calculate the distance by substituting the value of "t" in either of the two expressions we obtained earlier.
Distance = 5 kmph * (2/3 + 7/60) hours
= 5 * (40/60 + 7/60) km
= 5 * 47/60 km
= 235/60 km
= 3.92 km (rounded to two decimal places)
Therefore, the distance covered by Alka to reach school is approximately 3.92 km.