Question

If a scooterist drives at the rate of 24 km/hr from his home , he reaches his work place 5 minutes late. But if he drives at the rate of 30 km/hr , he reaches his work place 4 minutes early. Therfore , find the distance of his work place from his home.

Answer 1

Assume that he starts travelling to his workplace at the same time every day

Let the distance between his work place and home be 'd'

Let the actual time be 'x'

Distance = Speed * Time

Convert minutes into seconds as the units should be in kmph

As 24 kmph speed resulted in 5 minutes late, it is taken as increment 

d = 24(x + 5/60) ---------------(1)

As 30 kmph speed resulted in 4 minutes early, it is taken as decrement 
d = 30(x - 4/60) ----------------(2)

(1) and (2) are equal

=> 24(x + 5/60) = 30(x - 4/60)
=> 24x+2 = 30x-2
=> 30x - 24x = 2+2
=> 6x = 4
=> x = 2/3

Substitute the value of x in (1)
=> d = 24(2/3 + 5/60)
=> d = 24(9/12)
=> d = 18 km

The required answer is 18 km

Hope This Helps :)

Answer 2

Let the distance between workplace and his home be x.

The time is taken if he moves with a speed of 24km/hr = x/24 hr

                                                                                             = x/24 * 60

                                                                                             = 2.5.


The time is taken if he moves with a speed of 30km/hr = x/30 hr

                                                                                            = x/30 * 60

                                                                                            = 2x.


Difference in time = 2.5x - 2x

                               = 0.5x.


Now,

The time difference = 4 + 5

                                  = 9 minutes.


Therefore,

0.5x = 9

x = 18.


Therefore the distance = 18km.


Hope this helps!