Question 1102040
x represents the elapsed time in hours.
y represents the speed in miles per hour.
she starts off at 8 miles per hour and her speed decreased by 1.5 miles per hour every hour.


the equation to model this is y = -1.5 * x + 8


since she is traveling against the current, and the current is traveling at a constant rate of 3 miles per hour, then her overall speed is 3 miles per hour less than if she were rowing in a still current (not with nor against).


the equation to model this is y = -1.5 * x + 8 - 3


simplify this to get y = -1.5 * x + 5.


you can graph this equation and then mark her speed at every hour.


she will be traveling at a net speed of 0 miles per hour in 3 and 1/3 hours.


when she can't row anymore, she will be traveling at 3 miles per hour in the opposite direction (the speed of the current).


the graph looks like this.


<img src = "http://theo.x10hosting.com/2017/112002.jpg" alt="$$$">


the domain of this graph starts at x = 0 and ends at x = 5 and 1/3.


x can't be less than 0 because time can't be negative.
x can't be greater than 5 and 1/3 because she's completely exhausted and can't row anymore, either forward or backward.  she therefore can only drift backwards at the speed of the current.


her speed when she starts is a net 5 miles per hour.
8 miles per hour rowing against 3 miles per hour of current.


when her net speed is 0 miles per hour, she is rowing at a speed of 3 miles per hour against a current of 3 miles per hour.
this occurs in 3 and 1/3 hours.


when her net speed is -3 miles per hour, she is rowing at a speed of 0 miles per hour against a current of 3 miles per hour.
this occurs in 5 and 1/3 hours.


the coordinates of the graph are in (x,y) format.
x represents the hours she has been rowing.
y represents her net speed.


for example:


at (2,2), she has been rowing for x = 2 hours and her net speed is y = 2 miles per hour.


per the formula, y = -1/5 * 2 + 5 which results in y = -3 + 5 resulting in y = 2.