Two sailboats are traveling along the same path away from a dock, beginning from different locations at the same time. John's boat begins 20 miles from the dock and is 55 miles from the dock after 5 hours. The distance of Roberta's boat from the dock is represented by the function y = 6x + 10, where x represents time and y represents the distance from the dock. Which boat was farther from the dock at the beginning, and which traveled more quickly? A. John's boat was farther from the dock at the beginning, and it traveled more quickly B. John's boat was farther from the dock at the beginning, but Roberta's boat traveled more quickly C. Roberta's boat was farther from the dock at the beginning, but John's boat traveled more quickly D. Roberta's boat was farther from the dock at the beginning, and it traveled more quickly.
John is 7x+20
plz i need help now!!
To determine which boat was farther from the dock at the beginning and which boat traveled more quickly, we need to compare their initial distances from the dock and their rates of travel.
According to the information given, John's boat began 20 miles from the dock and was 55 miles from the dock after 5 hours. We can calculate John's rate of travel by dividing the change in distance (55 miles - 20 miles) by the time it took (5 hours): (55 miles - 20 miles) / 5 hours = 7 miles per hour.
Roberta's boat is represented by the function y = 6x + 10, where y represents the distance from the dock and x represents time. To determine Roberta's distance from the dock at the beginning, we substitute x = 0 into the function: y = 6(0) + 10 = 10 miles.
Comparing their initial distances from the dock, John's boat was farther at the beginning (20 miles) compared to Roberta's boat (10 miles).
Comparing their rates of travel, John's boat traveled at a speed of 7 miles per hour, while Roberta's boat has a constant rate of 6 miles per hour.
Therefore, the correct answer is option C: Roberta's boat was farther from the dock at the beginning, but John's boat traveled more quickly.