Justin boards a train a certain distance from the coast. The train moves directly away from the coast at a constant rate. After 14 hours on the train, Justin is 695 kilometers from the coast. After 18 hours, he is 879 kilometers from the coast.(a)Choose the statement that best describes how the time and Justin's distance from the coast are related. Then fill in the blank.As time increases, Justin's distance from the coast decreases.Justin'sdistancefromthecoastdecreasesatarateofkilometersperhour. As time increases, Justin's distance from the coast increases.Justin'sdistancefromthecoastincreasesatarateofkilometersperhour. (b)How far was Justin from the coast when he boarded the train?kilometers
Question
Justin boards a train a certain distance from the coast. The train moves directly away from the coast at a constant rate. After 14 hours on the train, Justin is 695 kilometers from the coast. After 18 hours, he is 879 kilometers from the coast.(a)Choose the statement that best describes how the time and Justin's distance from the coast are related. Then fill in the blank.As time increases, Justin's distance from the coast decreases.Justin'sdistancefromthecoastdecreasesatarateofkilometersperhour. As time increases, Justin's distance from the coast increases.Justin'sdistancefromthecoastincreasesatarateofkilometersperhour. (b)How far was Justin from the coast when he boarded the train?kilometers
Solution
(a) As time increases, Justin's distance from the coast increases. To find out the rate at which Justin's distance from the coast increases, we need to subtract the distance he was from the coast after 14 hours from the distance he was from the coast after 18 hours, and then divide that by the difference in time.
So, 879 kilometers - 695 kilometers = 184 kilometers. This is the distance Justin traveled in 18 hours - 14 hours = 4 hours.
Therefore, Justin's distance from the coast increases at a rate of 184 kilometers / 4 hours = 46 kilometers per hour.
(b) To find out how far Justin was from the coast when he boarded the train, we need to subtract the distance he traveled in 14 hours from the distance he was from the coast after 14 hours.
So, 695 kilometers - (14 hours * 46 kilometers per hour) = 695 kilometers - 644 kilometers = 51 kilometers.
Therefore, Justin was 51 kilometers from the coast when he boarded the train.
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