A student sarts for her school at the speed of 12 km / hr & reaches school 4 mins earlier than the asembily.next day she cycles at 10 km / hr & is late by 6 mins & missed assembly . Find distance b / w herschool & home
d/12 + 1/15 = d/10 - 1/10 ... 60 is LCD
5d + 4 = 6d - 6
12 km/hr * 1000 m/km * 1 hr/60 min = 200 meters/min
10 km/hr = 166.7 meters/min
distance = d
d = 200 (t-4) = 200 t - 800
d = 166.7(t+6) = 166.7 t + 1000
33.3 t = 1800
t = 54.1 minutes
d = 200(54.1) - 800 = 10,010 meters
= 10 km
check
200(54-4) = 10,000
167(54+6) = 10,000
her time difference is 10 minutes, or 1/6 hour
since distance = speed * time, and is the same both days, if she took t hours the first day, we have
12t = 10(t + 1/6)
t = 5/6 hr, or 50 minutes
so, the distance is
12km/hr * 5/6 hr = 10km
To find the distance between the student's home and school, we need to use the formula: Distance = Speed x Time.
Let's assume that the distance between the student's home and school is d kilometers.
First, let's find the time taken by the student to reach school when she walks at a speed of 12 km/hr.
Let's denote this time as T1.
We know that Time = Distance / Speed.
So, T1 = d / 12.
Now, let's consider the second scenario where the student cycles to school at a speed of 10 km/hr.
This time, she is late for the assembly by 6 minutes. Let's denote the time taken by the student to reach school as T2.
We know that Time = Distance / Speed.
So, T2 = d / 10.
Given that T2 + 6 minutes = T1 - 4 minutes.
To compare both times, we need to have them in the same units.
Converting minutes to hours, we have T2 + (6/60) hours = T1 - (4/60) hours.
Simplifying, T2 + 0.1 hours = T1 - 0.06667 hours.
T2 = (d / 10) = T1 - 0.06667.
Substituting the value of T1 from earlier, we get d / 10 = d / 12 - 0.06667.
To solve this equation, we can cross-multiply and simplify:
12d = 10d - 0.8.
12d - 10d = -0.8.
2d = -0.8.
d = -0.8 / 2.
d = -0.4.
However, a distance cannot be negative, so there seems to be an error in the information provided. Please check the given values and re-calculate.