What distance did this person travel?

Question

If a person travels from home to work at a speed of 42 MPH and arrives 5 minutes early. Also, When that person travels from home to work at 30 MPH and arrives 5 minutes late. What distance did that person travel?

Answer 1

Let´s put the velocitys in Miles/min
distance = 42/60 *(t-5) and
distance = 30/60 *(t+5)
Dividing 1= 42/30 (t-5)/(t+5)
30t+150 =42t -210 so 12 t = 360 and t=30minutes
d= 35/2 =17.5 miles

Answer 2

Supoose the ideal time duration is "T".
Also the speed 42 MPH = 42/60 Mile Per Minute
So the distance traved by him his = 42/60*(T-5)
Second time speed 30 MPH = 30/60 Mile Per Minute
Distance = 30/60*(T+5)

Hence, 42/60*(T-5) = 30/60*(T+5)
=> 42(T-5) = 30(T+5)
=> 42T - 210 = 30T + 150
=> (42-30)T = 150+210
=> 12T = 360
=> T = 30
So the standard time duration is 30 seconds.
Now, put this value in any of the equations above and get the distance;

42/60*(30-5) = Distance

Distance = 42/60*25
= 25*7/10 = 175/10
= 17.5 Miles