Let us assume that the total length of the highway = X
From the question, we know that the workers have completed 2/5 of the total length. Then the distance upto which work is completed = 2X/5
On completing another 7.5 miles, the work would be complete by half.
So
2X/5 + 7.5 = X/2
(X/2) - (2X/5) = 7.5
(5X/10) - (4X/10) = 7.5
(5X -4X)/10 = 7.5
X/10 = 7.5
X = 7.5 * 10
= 75
So the total length of the highway under construction is 75 miles.
