Answer:
Speed limit = 55 mph.
Step-by-step explanation:
Suppose the time that he travels 5 mph below the speed limit is t hours.
Speed = distance / time so v - 5 = 10/t where v = the speed limit.
When he travels 15 mph below the speed limit we have the equation
v - 15 = 10 / t + 1/30......(1) ( because 2 minutes = 1/30 of an hour).
v - 5 = 10/t ..................(2)
Simplifying equation (1):-
(v - 15)( t + 1/30) = 10
vt + v/30 - 15t - 0.5 = 10
30vt + v - 450t - 15 = 300
v = (450t + 315) / (30t + 1)......... (3)
From equation (2):
vt - 5t = 10
v = 5t+ 10 / t .........(4)
Equating equations (3) and (4):-
(5t + 10) / t = (450t + 315) / (30t+1)
(5t + 10)(30t + 1) = 450t^2 + 315t
150t^2 + 305t + 10 = 450t^2 + 315t
300t^2 + 10t - 10 = 0
solving this gives t = 1/6 hour.
So from equation 2, v = 10 / 1/6 - 5
= 60 - 5 = 55 mph (answer).
