Jamie recently drove to visit her parents who live 720 miles away. on her way there her average speed was 14 miles per hour faster than on her way home (she ran into some bad weather). if jamie spent a total of 30 hours driving, find the two rates.

Jamie spent 30 hours driving to and from her parents house.

Total distance of one trip= 720 miles.
Let x be her speed when she was travelling back home. So her speed on her way to her parents home will be x + 14

Distance = Speed x Time
So,
Time = Distance/Speed

While travelling towards her parents house, the equation for time will be:

Time = 

While travelling back to her house, the equation for time will be:

Time = 

It took her a total of 30 hours, so we can write:



Since x represents the speed and it cannot have a negative value we ignore x= - 8.

So, Jamie's speed on her way back home was 42 miles per hour. And her speed on her way to her parents home was 42+14 = 56 miles per hour

The time she spent driving towards her parent home = 720/56 = 12 hours and 51 minutes

The time she spent driving towards her home = 720/42 = 17 hours and 9 minutes