Word problem: A new photocopier can make 72 copies in 2 min. When the older photocopier is operational, the two photocopiers together can make 72 copies in 1.5 min. How long would it take the older photocopier to make 72 copies working alone? Show work.
rate of new = 72/2 copies/min
rate of old = 72/x copies/min
combined rate = 72/2 + 72/x
= (72x + 144)/(2x) copies per min
72/(72x+144)/(2x)) = 1.5
72(2x)/(72x+144) = 1.5
144x = 108x + 216
36x = 216
x = 6
rate of old machine = 72/6 or 12 copies/minute
Thanks much, that helps a lot.
or, consider this as the usual work problem, where the job is to make 72 copies.
1/1.5 = 1/x + 1/2 = 1/1.5
1/x = 2/3 - 1/2
1/x = 1/6
x = 6
It would have been a little more interesting if the number of copies given for each machine had been different. You might play around with that if you're curious.
Melissa Stone was just hired as a nurse at a hospital where she will earn $45,000 per year. If she receives a 6% raise each year, how much total money will she earn over the next 10 years?
$477000
To solve this word problem, we can use the concept of rates.
Let's assume that the older photocopier can make x copies in one minute when working alone.
From the given information, we know that the new photocopier can make 72 copies in 2 minutes. Therefore, the rate of the new photocopier is 72 copies / 2 minutes = 36 copies/minute.
We are also given that when the two photocopiers (new and old) work together, they can make 72 copies in 1.5 minutes. Therefore, their combined rate is 72 copies / 1.5 minutes = 48 copies/minute.
Now, let's set up the equation to represent the combined rate of the two photocopiers:
Rate of new photocopier + Rate of old photocopier = Combined rate of both photocopiers
36 copies/minute + x copies/minute = 48 copies/minute
Adding the two rates together, we can simplify the equation to:
36 + x = 48
Now, we can solve for x:
x = 48 - 36
x = 12
So, the older photocopier can make 12 copies in one minute when working alone.
To find out how long it would take the older photocopier to make 72 copies working alone, we can use the rate we just found.
Time = Number of Copies / Rate
Time = 72 copies / 12 copies/minute
By canceling out the units, we find that:
Time = 72 / 12
Time = 6 minutes
Therefore, it would take the older photocopier 6 minutes to make 72 copies working alone.