Answer:
John's boat was farther from the dock at the beginning, but Roberta's boat traveled more quickly.
Step-by-step explanation:
Let's start with the first part of the question: whose boat started farther away from the dock? The question specifically tells us that John's boat started 20 miles away, but we have to do a little digging to find out how far away Roberta's started. To find her boat's distance, you want to look at the equation: (x=time and y=distance from dock) y = 6x + 15. Assuming that x is representing her time in hours, we can set its value to zero, meaning that she has not traveled at all, and is therefore where she started. By doing this, we find that her distance from the dock before she started is 15 miles! This means that John's boat was farther from the dock at the beginning.
Next, we'll figure out who traveled more quickly. The problem states that John is 45 miles from the dock after 5 hours, and that he started 20 miles out. This means that we must subtract 20 from 45, giving us 25, in order to understand how far he traveled (not just how far away from the dock he is). From here, there are technically two ways to solve, but I find the one I am going to show you easier and quicker!
Begin by dividing 25 by 5 in so that you know how many miles per hour he is going, then compare it to Roberta's. To compare, you must look at the equation and note that however many hours she has spent moving is going to be multiplied by 6 in order to find how many miles she traveled during that time (we add 15 after that to account for the miles away from the dock that she started with). This shows us that John was traveling 5 mph, while Roberta is traveling 6 mph, meaning she is faster.
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