If Seeta walks from her home to school at a speed of 4 km/h, she is late by 9 min. If she walks at a speed of 6 km/h, she reaches the school 6 min early. What is the distance between her school and her home?

If Seeta walks from her home to school at a speed of 4 km/h, she is late by 9 min. If she walks at a speed of 6 km/h, she reaches the school 6 min early.

Let T is the actual time taken to reach the destination by Sita.

case 1 : if the speed of Sita , u = 4 km/h , she reaches her destination 9 min late .

e.g., distance between Sita and destination point , S = speed of Sita × time taken

$$= 4 \times (T + \frac{9}{60})$$ km

so, $$S = 4(T + \frac{9}{60})$$   .... (1)

case 2 : if the speed of Sita, v = 6 km/h , she reaches her destination 6 minutes early.

$$= 6 × (T - \frac{6}{60})$$ km

so,$$ S = 6(T - \frac{6}{60})$$         ....(2)

from equations (1) and (2),

$$4(T + \frac{9}{60}) = 6(T - \frac{6}{60})$$

$$=4T + \frac{36}{60} = 6T - \frac{36}{60}$$

$$=2T =\frac{72}{60}$$

$$T = \frac{3}{5}$$

or, T = 36 mins

putting $$T = \frac{3}{5}$$ in equation (1),

$$S = 4(\frac{3}{5} + \frac{9}{60}) = 3 $$kms