Plz send some backup because i don’t get this problem

You know the relationship between speed and distance and time, because it is written on every speed limit sign you pass:

... speed = miles/hour = distance/time

You don't know the distance, but you know speed and time. Solving the above equation for time, we get

... time = distance/speed

You don't know the distance, but you can write an equation based on what you do know.

... time going = distance/460

... time returning = distance/500

... 4.8 = time going + time returning = distance/460 + distance/500

Performing the addition, you get

... 4.8 = distance(500 + 460)/(500·460)

And solving for distance, you get

... distance = 4.8·500·460/(500+460) = 1150

Putting this into our expressions for time going and returning, we have

... time going = 1150/460 = 2.5 . . . hours

... time returning = 1150/500 = 2.3 . . . hours

Once you realize the travel times are inversely proportional to the speeds, you can see that ...

... time going : time returning = 500 : 460 = 25 : 23 . . . . . the reverse of the speed ratio

That is, the time going is 25/(25+23) = 25/48 of the total time, so is

... (25/48)·4.8 hours = 2.5 hours

Of course, the return time is (23/48)·4.8 = 2.3 hours, or the difference

... 4.8-2.5 = 2.3 hours.