Using the example above, the new high way will be a total of 54 miles long. will the highway be finished in 8 months

The above problem is incomplete. I have read the whole problem.

Given:
54 miles long highway
5 3/5 miles constructed per month.

Will the highway be finished in 8 months?

5 3/5 ⇒ ((5*5)+3)/5 = 28/5

28/5 * 8/1 = 28*8 / 5*1 = 224/5 = 44.8 miles or 44 4/5 miles

No. The highway can not be finished in 8 months. Only 44.8 miles or 44 4/5 miles will be constructed by that time.

54 ÷ 28/5 = 54 * 5/28 = 54*5 / 28 = 270 / 28 = 9.64 months or 9 18/28 or 9 9/14 months must be spend to complete the highway.