Question

ravi is on a train trip to field city. the train is traveling at a constant rate. after 6 hours on the train, there are 624 kilometers remaining to field city. after 11 hours, there are 369 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 \\(\square\\) kilometers per hour.
∘as time increases, the distance remaining to field city increases.
the distance remaining to field city increases at a rate of \\(\square\\) kilometers per hour.

(b) how far was ravi from field city at the beginning of the trip?

\\(\square\\) kilometers

Explanation:

Step1: Calculate time difference

$11 - 6 = 5$ hours

Step2: Calculate distance change

$624 - 369 = 255$ kilometers

Step3: Find rate of distance decrease

$\frac{255}{5} = 51$ kilometers per hour

Step4: Calculate initial distance

Let $d$ = initial distance. Use $d - 51\times6 = 624$
$d = 624 + 51\times6 = 624 + 306 = 930$ kilometers

Answer:

(a) As time increases, the distance remaining to Field City decreases.
The distance remaining to Field City decreases at a rate of 51 kilometers per hour.
(b) 930 kilometers