Question

if a scooterist drives at the rate of 24km/hour from his home, he r workplace 5 minutes late. but if he drives at the rate of 30 km/hour, he reaches his workplace 4 minutes early. find the distance of his work place from his home?

Answer 1

i hope i was a help to u

Answer 2

24 kmph = 24 × 5/18 m/s = 120/18 m/s
30 kmph = 30 × 5/18 m/s = 150/18 m/s

Let the ideal time to reach the work place be t (in seconds) and distance between home and workplace be d

Speed = Distance / Time

In first case
120/18 = d / (t + (5 × 60))
120/18 = d / (t + 300) …………(1)

In second case
150/18 = d / (t - (4 × 60))
150/18 = d / (t - 240) ……………(2)

Divide equation (1) by (2)
120/150 = (t - 240) / (t + 300)
12 / 15 = (t - 240) / (t + 300)
12t + 3600 = 15t - 3600
3t = 7200
t = 2400 seconds

Substitute t = 2400 seconds in equation (1)
120 / 18 = d / (2400 + 300)
d = (120 × 2700 / 18) m
d = 18000 m
d = 18 km

∴ Distance between work place and home is 18 km