Question

A teacher starts from his house to school at a fixed time on scooter.if he goes 36km/h he is late by 5 minutes. if he goes at 45 km/h he reaches 3 minutes earlier.find distance between his house to school

Answer 1

36 kmph = 36000/60 m/min = 600m/min

 

45kmph = 45000/60 m/min = 750m/min.

 

If the normal time is t and distance between home and school is d, then

 

At 600m/min (36kmph), time taken is d/600 = t + 5 min

 

And at 750m/min (45kmph), time taken is d/750 = t-3

 

Thus, d = 600*t+3000 = 750*t-2250

 

75t-60t = 3000+2250 = 5250

 

Therefore, 150t = 5250 or t = 35mins.

 

Thus, the normal time taken is 35 minutes and substituting it in d/60 = t+5, we get

 

d/600 = 40 or d = 40*600 = 24000 m = 24km.

 

Therefore, the distance between house and school is 24km.