Algebra Linear Functions question

Question

Jay is driving home from his family's lake house which is 398 miles away from where he lives. He drives at an average speed of 58 miles per hour. a. Write a linear function that represents Jay's total distance from home, D(t), after t hours. b. How far away from home is Jay after driving for 2 hours? C. How many hours will it take for Jay to get home?

Answer 1

a. Distance travelled in time t is= 58*t. Total distance to cover is 398 miles. Therefore the distance from home = 398 - f8t. The linear equation can be represented as d, which is the distace from home as d= 398 - 58t miles.

b. After t = 2 hours d = 398 - 58*2 = 398 - 116 = 282 miles from home

c. Hours to reach home from the starting point is the number of hours to cover distance of 398. Thus when Jay reaches home the disntnace from home is 0 miles. Substituing in the linear equation: d = 398 - 58t where d = 0. Thus, 0 = 398 - 58t i.e. t = 398/58 = 6.86 hours