Question

Ron's recycle shop had an old paper-shredding machine. Business was good, so he bought a new paper-shredding machine. The old machine could shred a truckload of paper in 4 hours. The new machine could shred the same truckload in 2 hours. How long will it take to shred the same truckload of paper if Ron runs both shredders at the same time?

Answer 1

Answer: 1 hour 20 minutes

Step-by-step explanation:

Given : The old machine could shred a truckload of paper in 4 hours.

Rate of work done by old machine = $\dfrac{1}{4}$

The new machine could shred the same truckload in 2 hours.

Rate of work done by new machine = $\dfrac{1}{2}$

Let 't' be the time taken by both of them working together , then we have the following equation:-

$\dfrac{1}{t}=\dfrac{1}{4}+\dfrac{1}{2}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1+2}{4}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{4}\\\\\Rightarrow t=\dfrac{4}{3}=1\dfrac{1}{3}\ \text{ hours}$

Since 1 hour = 60 minutes

Then, $\dfrac{1}{3}\ \text{ hours}=\dfrac{1}{3}\times60=20\text{ minutes}$

Hence, it will take 1 hour 20 minutes to shred the same truckload of paper if Ron runs both shredders at the same time.

Answer 2

It will take 4/3 hours to shred the same truckload of paper if Ron runs both shredders at the same time

From the question, we have the following parameters

Old machine = 4 hours

New machine = 2 hours

Represent the time that they shred  together with t.

So, we have:

$\frac 1t = \frac 14 + \frac 12$

Multiply through by 4

$\frac 4t = 1+ 2$

Evaluate like terms

$\frac 4t = 3$

Solve for t

$t = \frac 43$

Hence, it will take 4/3 hours to shred the same truckload

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