Question 1102040: Shelly is rowing a boat upstream. The river is flowing at a speed of 3 miles per hour. Sharon starts rowing at a speed of 8 miles per hour, but as she gets tired her speed decreases (at a rate of 1.5 miles per hour, every hour).
Graph the equation that fits the description, where y represents Sharon's speed and x represents the time elapsed since the start of her workout.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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.
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