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.
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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.
84 feet because you would just add the 70 and 14 together
Let the price of the 3rd card be c. Now we can write the equation:
c + (c + 20) + (c + c + 20) = 160 .........(1)
Simplifying the left hand side of equation (1), we get:
4c + 40 = 160 .........(2)
Subtracting 40 from both sides of equation (2) gives:
4c = 120
from which c = $30.
Therefore the price of the second card = 30 + 20 = $50
and the price of the first card = 30 + 50 = $80.
