An impact printer prints 1 page using regular type and 3 pages using bold type in 23 seconds. If the printer prints 2 pages using regular type and 4 pages using bold type in 34 seconds, how long does it take to print 1 page for each typeface?
Use the rate equation
page= rate*time
Time= pages/rate where rate is pages/sec
23=1/rp + 3/rb and
34=2/rp + 4/rb
This is easiest solved by solving for 1/rp and 1/rb
multiply the numerator by 2, then subtracting,
46-34= (1/rb)(6-4) solve for 1/rb, that give you time per bold page, then go back and solve for 1/rp
To solve this problem, let's assign some variables:
Let's say the time it takes to print 1 page using regular type is "r" seconds.
And the time it takes to print 1 page using bold type is "b" seconds.
Now let's set up two equations using the given information:
1) From the first scenario:
1r + 3b = 23 --> Equation 1
2) From the second scenario:
2r + 4b = 34 --> Equation 2
Now we have a system of equations. To solve it, we can use either substitution or elimination method.
Let's use the elimination method:
Multiply Equation 1 by 2:
2r + 6b = 46 --> Equation 3
Now, subtract Equation 2 from Equation 3:
(2r + 6b) - (2r + 4b) = 46 - 34
2r + 6b - 2r - 4b = 12
2b = 12
b = 12/2
b = 6
So, it takes 6 seconds to print 1 page using bold type.
Now we can substitute the value of "b" into Equation 2 to find the value of "r":
2r + 4(6) = 34
2r + 24 = 34
2r = 34 - 24
2r = 10
r = 10/2
r = 5
Therefore, it takes 5 seconds to print 1 page using regular type.
In conclusion, it takes 5 seconds to print 1 page using regular type and 6 seconds to print 1 page using bold type.