Question

walking at a speed of 5 km per hour, a student is 30 min late for school. but if he goes at 6 km per hour then he is late by just 5 minutes what is the distance between home and school

Answer 1

Let the time taken to reach be 'y' hours.
Let the distance be 'x' km.

ATQ

Speed = Distance / Time

Time = Distance / Speed

=> y + (30 / 60) = x / 5

y + 1 / 2 = x / 5

(2y + 1) / 2 = x / 5 (Taking LCM of y and 1/2)

2x = 10y + 5 (Cross Multiplying)

2x - 10y = 5 (eq. 1)


=> y + 5 / 60 = x / 6

(12y + 1) / 12 = x / 6

12x = 72y + 6

12x - 72y = 6

Taking 6 as common on both sides.

6 (2x - 12y) = 6 (1)

= 2x - 12y = 6 (eq. 2)


Using (eq. 1) and (eq. 2)

=> 2x - 10y = 5
2x - 12y = 1
(-) (+) (-)
_____________
2y = 4
_____________

y = 2

Using (eq. 1)

2x - 10(2) = 5

2x - 20 = 5

2x = 25

x = 12.5

Therefore, the distance between the school and home is 12.5 km.