Shen is on a train trip to Treevale City. The train is traveling at a constant rate. After 9 hours on the train, there are 415 kilometers remaining to Treevale City. After 16 hours, there are 100 kilometers remaining to Treevale City.
a) Choose the statement that best describes how the time and the distance remaining to Treevale City are related. Then fill in the blank.
As time increases, the distance remaining to Treevale City decreases.
the distance remaining to treevale city decreases at a rate of _ kilometers per hour.
As time increases, the distance remaining to Treevale City increases.
the distance remaining to treevale city increases at a rate of _ kilometers per hour.
(b)How far was Shen from Treevale City at the beginning of the trip?
a) The statement that best describes how the time and the distance remaining to Treevale City are related is: As time increases, the distance remaining to Treevale City decreases.
The distance remaining to Treevale City decreases at a rate of 46 kilometers per hour.
b) To find out how far Shen was from Treevale City at the beginning of the trip, we need to subtract the distance remaining after 9 hours (415 kilometers) from the total distance to Treevale City.
Distance at the beginning of the trip = Total distance - Distance remaining after 9 hours = 415 km + Distance remaining after 9 hours.
Since the train is traveling at a constant rate, the distance remaining is decreasing at a rate of 46 kilometers per hour. Therefore, the distance remaining after 9 hours is 9 hours * 46 kilometers per hour = 414 kilometers.
Distance at the beginning of the trip = 415 km + 414 km = 829 kilometers.
So, Shen was 829 kilometers from Treevale City at the beginning of the trip.