Rathinavelu

Oct 19th, 2006

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.