Question

rafael is on a train trip to field city. the train is traveling at a constant rate. after 7 hours on the train, there are 576 kilometers remaining to field city. after 13 hours, there are 264 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.
the distance remaining to field city decreases at a rate of □ kilometers per hour.
○as time increases, the distance remaining to field city increases.
the distance remaining to field city increases at a rate of □ kilometers per hour.
(b) how far was rafael from field city at the beginning of the trip?
□ kilometers

Explanation:

Step1: Identify rate of distance change

Calculate distance change: $576 - 264 = 312$ km
Calculate time change: $13 - 7 = 6$ hours
Rate: $\frac{312}{6} = 52$ km/h

Step2: Confirm relationship type

Since remaining distance drops from 576 to 264 km as time increases, the distance decreases over time, at 52 km/h.

Step3: Find initial distance

Distance covered in 7 hours: $52 \times 7 = 364$ km
Initial distance: $364 + 576 = 940$ km

Answer:

(a) As time increases, the distance remaining to Field City decreases.
The distance remaining to Field City decreases at a rate of 52 kilometers per hour.
(b) 940 kilometers