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Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.
<h3>What is the relation between velocity, distance and time?</h3>Velocity is distance divided by time, hence:
v = d/t
A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:
12 + r = 46/t
r = 46/t - 12
Downstream, the time is of t + 2 hours, hence:
12 - r = 46/(t + 2)
r = 12 - 46/(t + 2)
Hence, equaling the values for r:
46/t - 12 = 12 - 46/(t + 2)
46/t + 46/(t + 2) = 24
92t + 92 = 24t² + 48t
24t² - 44t - 92 = 0
Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:
r = 46/t - 12 = 46/3 - 12 = 3.33 mph.
More can be learned about the relation between velocity, distance and time at brainly.com/question/28155966
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Answer:
Area of ΔDEF = 12 in²
Step-by-step explanation:
Since they are similar, we have to find the scale factor
Scale Factor =
Scale Factor = 4/2
Scale Factor = 2
<u><em>This means The area of ΔABC is 2 times the area of ΔDEF</em></u>
So,
ΔABC = 2(ΔDEF)
Where Area of ΔABC = 24 in²
24 = 2(ΔDEF)
Dividing both sides by 2
=> Area of ΔDEF = 12 in²