Kevin is on a train trip to Field City. The train is traveling at a constant rate. After 9 hours on the train, there are 530 kilometers remaining to Field City. After 16 hours, there are 180 kilometers remaining to Field City.(a)Choose the statement that best describes how the time and the distance remaining to Field City are related. Then fill in the blank.As time increases, the distance remaining to Field City decreases.ThedistanceremainingtoFieldCitydecreasesatarateofkilometersperhour. As time increases, the distance remaining to Field City increases.ThedistanceremainingtoFieldCityincreasesatarateofkilometersperhour. (b)How far was Kevin from Field City at the beginning of the trip?kilometers
Question
Kevin is on a train trip to Field City. The train is traveling at a constant rate. After 9 hours on the train, there are 530 kilometers remaining to Field City. After 16 hours, there are 180 kilometers remaining to Field City.(a)Choose the statement that best describes how the time and the distance remaining to Field City are related. Then fill in the blank.As time increases, the distance remaining to Field City decreases.ThedistanceremainingtoFieldCitydecreasesatarateofkilometersperhour. As time increases, the distance remaining to Field City increases.ThedistanceremainingtoFieldCityincreasesatarateofkilometersperhour. (b)How far was Kevin from Field City at the beginning of the trip?kilometers
Solution
(a) As time increases, the distance remaining to Field City decreases. The distance remaining to Field City decreases at a rate of kilometers per hour.
To find the rate of decrease, we subtract the remaining distance after 16 hours (180 km) from the remaining distance after 9 hours (530 km), and then divide by the difference in time (16 hours - 9 hours = 7 hours).
So, (530 km - 180 km) / 7 hours = 350 km / 7 hours = 50 kilometers per hour.
(b) To find the initial distance from Field City, we need to add the distance the train traveled in the first 9 hours to the remaining distance after 9 hours.
The train travels at a rate of 50 km/hour, so in 9 hours it travels 50 km/hour * 9 hours = 450 km.
Adding this to the remaining distance after 9 hours (530 km), we get 450 km + 530 km = 980 kilometers.
So, Kevin was 980 kilometers from Field City at the beginning of the trip.
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