1 shredder shreds 1 truck load in 4 hours, the other shredder shreds 1 truck load in 2 hours. How long does it take for both shredders working together to shred

Question

1 shredder shreds 1 truck load in 4 hours, the other shredder shreds 1 truck load in 2 hours. How long does it take for both shredders working together to shred 1 truck load?

Answer 1

Hi John,

 

To solve this type of question, you first figure out the fraction of the load that each shredder does in one hour:

 

Shredder 1 does 1/4 truck load in one hour and shredder 2 does 1/2 truck load in one hour.

 

Now add them up:  Both trucks do 1/4 + 1/2 = 1/4 + 2/4 ==3/4 of a truck load in one hour.

 

Now think about how long it would take both of them together to do one truck load if they finished 1/2 a truckload in one hour . . . it would be 2 hours which you get by taking the reciprocal of 1/2

 

So in the above question, it would take the reciprocal of 3/4 hours for them to shred one truck load or 1 1/3 hours or 1 hours and 20 minutes.

 

Dan