Question

Jack travels to work on the Eastern Freeway. He notices that the difference in time between if he drives 5 mph below the speed limit and if he drives 15 mph below the speed limit is 2 minutes. Given that the distance for which he uses the freeway is 10 miles, find the speed limit of the freeway.

Answer 1

Speed limit = 55 mph.

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).