Answer: 25 minutes
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Step-by-step explanation:
x = time that has gone by in minutes
y = distance from the hare's starting location
The slope of this line is m = 2 which is the tortoise's speed in feet per min. The y intercept is b = 100 as this is the tortoise's starting distance from the hare. Plug these into y = mx+b to get y = 2x+100.
The equation for the tortoise is y = 2x+100
The hare has a slope of m = 6, which is its speed, and a y intercept of b = 0. We go from y = mx+b to y = 6x+0 or just y = 6x.
The equation for the hare is y = 6x.
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Graph y = 2x+100 and y = 6x. Locate the intersection point. You should find it is (25,150). So this is why 25 is the answer.
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Alternatively, you can use algebra to solve for (x,y)
y = 2x+100
6x = 2x + 100
6x-2x = 100
4x = 100
x = 100/4
x = 25
It takes 25 minutes for the hare to catch up to the tortoise
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After x = 25 minutes go by, the hare has traveled
d = r*t = 6*25 = 150 feet
and in the same time, the tortoise has traveled
d = r*t = 2*25 = 50 feet
the difference 150 - 50 = 100 matches up with the 100 ft head start the tortoise got.