Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
The range of possible values for the volume of the boxes would be 1200 - 1800 cubic inches
The dimensions of the rectangular cardboard boxes are given as
Case I
Length = 20 inches
breadth = 15 inches
Height = 4 inches
Volume of the rectangular cardboard box in case I = Length x breadth x breadth
= 20 x 15 x 4
= 1200 cubic inches
Similarly,
Case II
Length = 20 inches
breadth = 15 inches
Height = 6 inches
Volume of the rectangular cardboard box in case I = Length x breadth x breadth
= 20 x 15 x 6
= 1800 cubic inches
To learn more about volume, here
brainly.com/question/1578538
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I believe the answer is 5,473. Sorry if i'm wrong.
Answer:
y=2x+4
Step-by-step explanation:
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