Question 678791
Let t = time it takes to travel a distance of d miles (and be on time)


So to be an hour early, it would mean that you travel 1 hour less than normal, which means that you spend t-1 hours on the road.


To be an hour late, you add 1 to t to get t+1 hours.


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Being 1 hr early


d = rt


d = 60t


d = 60(t-1)


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Being 1 hr late


d = rt


d = 30t


d = 30(t+1)


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Equate the two and solve for t



60(t-1) = 30(t+1)


60t-60 = 30t+30


60t-30t = 30+60


30t = 90


t = 90/30


t = 3


So if you arrive on time, then you will spend 3 hours on the road. Being early means you only spend 2 hours on the road and being late means you spend 4 hours on the road.


Use this to find d


d = 60(t-1)


d = 60(3-1)


d = 120


Therefore, the distance is <font color="red">120 miles</font>.