Initially the the car is travelling for 2 hours and 10 minutes delay due to flat tire. the rest of the distance is covered with the speed of 30 miles/hour, but they are late by 1/2 an hour.

Total distance = d1 + d2, v2 = speed with which d2 is travelled if the car is not punctured.

Equation 1:  2 + (10 minutes delay) + d2/30 = t0 + ( 1/2 an hour late)

                 2 + 1/6 + d2/30 = t0 + 1/2  -----------> 1

When the car is not punctured the car would have travelled with the same speed.

Equation 2:  2 + d2/V2 = t0 + ( 15 minutes delay )       where v2 = d1/2  

                 2 + 2d2/d1 = t0 + 1/4        -------------> 2

Sub 2 from 1 : 1/6 + d2/30 - 2d2/d1 = 1/4

                    5d1 + 120d2 = 2d1d2

Let d2 = 5 :    5d1 = 120*5

                      d1 = 120

Therefore the total distance will be 125 miles ( this is one of the answers )

we can substitute from 3 to 59 for d2 and can find many solutions for this problem.