Question 939380
Two parallel time-lines helped in understanding the timing situation.


A___________0 mph for 0.00556 hour__________30 mph for x hour


B__________15 mph for x+0.00556 hour




A_________________{{{0*(0.00556)+30x}}}


B_______________{{{15(x+0.00556)}}}


Another arrangement is time for B is another variable, y.
Time quantity of y can be found.
{{{(1/4)/15=1/60}}}, hour




<b>Better understanding happens HERE:</b>


Truck B having 20 seconds headstart, traveled 15*(0.00556) miles, BEFORE truck A began.
Truck B reached position 0.08333333 miles from starting point.


Now consider new time arrangement.
At time 0, A is at position 0, and B is at position 0.0833333.



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Data table and using distances according to the positions from departure to 0.25 trip distance.


_____________________speed___________time_____________distance
A_____________________30_____________(1/4)/30_________1/4
B_____________________15_____________({{{t}}})_______________{{{0.25-0.08333}}}


Cleaning that a little bit,

_____________________speed___________time_____________distance
A_____________________30_____________{{{1/120}}}___________1/4
B_____________________15_____________({{{t}}})____________{{{0.25-0.08333}}}


Solve for travel time of truck B, and then compare to the travel time of truck A.  {{{t=(0.25-0.08333)/15}}}


The least time quantity corresponds to the truck which arrived first.