i need to fill a dam . i know 9 large can fill it in 4 hrs and 6 small can fill it in 8hrs . how long will it take to fill it if i have 4large and 8 samll hoses

Question

 please show your work

Answer 1

1 dam = 9 large hoses * 4 hrs

 

1/9 dam = 1 large hose * 4 hrs  <--- divides both sides by 9

 

1 dam = 1 large hose * 36 hours <-- multiplies both sides by 9

 

1/36 damn = 1 large hose * 1 hour

 

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LIkewise, repeating the same argument,

1 small hose can fill the dam in 48 hours

 

So 1/48 damn = 1 small hose * 1 hour

 

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4 large hoses and 8 small hoses will fill

 

8x4/48 dam  in 1 hour

 

32/48  dam in 1 hour

 

2/3 dam in 1 hour

 

So they can fill the dam in 3/2 hour = 1.5 hours = 1 and 1/2 hours = 1 hour and 30 minutes