a tire shop had filed 2 2/3 tires with air. It took a small air compressor 3 1/5 seconds to fill them up. How long will it take to fill 8 tires?

Question

 it is hard.

Answer 1

step #1: writes the proportion as tires vs time in seconds to fill them with air

(2 + 2/3) in proportion to (3 + 1/5)

equals

8 in proportion to ?

step #2: rewrites the mixed fractions as top-heavy improper fractions:

2 + 2/3 = 8/3....

3 + 1/5 = 16/5

step 3: rewrites the proportion using the top-heavy improper fractions

8/3 in proportion to 16/5

equals

8 in proportion to ?

step 4: cross multiplies: (8/3) * ? = (16/5)*8

step 5: solves (8/3) * ? = (16/5)(8/1)

step 6: multiplies both sides by (3/8)

(3/8)(8/3)*? = (3/8)(16/5)(8/1)

? = (3 * 16*8)/(8*5*1)

= (3*16)/(5*1) <--- 8 cancels out

= 48/5

= 9 + 3/5 seconds

it will take 9 and 3/5 seconds to inflate 8 tires, assuming the air compressor does not malfunction

and maintains the same speed

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Here is another way to do the SAME PROBLEM!!!

It took the air compressor 3 +1/5 seconds to inflate 2+2/3 tires....

Dividing them....

(3 + 1/5) seconds DIVIDED BY (2 + 2/3) tires =

(16/5) DIVIDED BY (8/3) seconds per tire =

(16/5)(3/8) seconds per tire =

48/40 seconds per tire =

6/5 seconds per tire

Therefore, the air compressor shall inflate 8 tires in 8 * (6/5) = 48/5 seconds = 9 + 3/5 seconds

We are also assuming the tires are the same size.....