Answer:
Let x be the first piece, y the 2nd, Z the 3rd
You know all of the pieces together make 24 thus,
24 = x + y + z
The second piece is 2 times longer than the 1st so,
y = 2x
The 3rd is 5 times longer
z = 5x
Replace them in the equation of the beginning
24 = x + 2x + 5x
24 = 8x
x = 3 (First piece)
y = 6 (Second Piece)
z = 15 (Third Piece)
270 miles apart. You can figure this out by dividing 60 by 2 to figure out how much miles 1 inch is and then, multiplying the number (30) by 9.
Answer:
Time machine one = 3.56
Time machine two = 4.56
Step-by-step explanation:
Let machine 2 do the job in x hours
Let machine 1 do the job in x - 1 hours.
The general formula for this problem is
Time = A*B/(A + B)
Givens
Time = 2 hours
B = x hours alone
A = x - 1 hours alone.
#################
x *( x - 1)
======= = 2
(x + x - 1)
(x^2 - x)/(2x - 1) = 2
x^2 - x = 2(2x - 1)
x^2 - x = 4x - 2
x^2 - 5x + 2 = 0
a = 1
b = - 5
c = 2
This gives 2 roots
x = 4.56
x = 0.43
The second root will not work because when 1 is subtracted from 0.43 the time give will be minus, which won't work.
Time for machine 2 is 4.56
The time for machine 1 is 3.56
Check
(A * B)/(A + B) = 2
A = 4.56
B = 3.56
Time = 4.56*3.56/(4.56 + 3.56)
Time = 16.2336/(8.12)
Time = 1.9992
The rounding error in the check comes from the rounding error in the times.
The first answer is B
The second answer is D
