small word problems

Question

If two brothers work together they can change the oil in the family car in 3 minutes. If it takes the older brother 12 minutes to change the oil alone, how long does it take for the younger brother to change the oil?

Answer 1

Hi, Madison.  

 

The equation we need to use is 1/T_older+ 1/T_younger= 1/T_total

 

We can plug in 3 for T_total (the total amount of time for both to change the oil) and 12 for T_older (the time it takes the older brother to change the oil).  We get: 

 

1/12 +1/T_younger= 1/3 

 

Subtracting 1/12 from both sides, we get: 

 

1/T_younger = 1/3 - 1/12

 

The simplify the right hand side, we need to find a common demoninator.  12 words as a common denominator, so we can rewrite it as: 

 

1/T_younger = 4/12 - 1/12 = 3/12 = 1/4

 

1/T_younger = 1/4

 

We can "flip" both sides of the equation to get T_younger = 4 minutes.  

 

This answer makes sense because each brother alone is slower than both brothers together.  

 

I hope that helps!  Good luck with your studies.  

 

Alix