Question

Tim and Tom are painters. Tim and Tom are painting a crate. Tom paints 10 sq ft per minute. They painted a particular crate in 1 day. Tim uses a sprayer and is 3.5 times as fast as Tom. How long would it take them to paint a crate with twice the volume and of similar shape? Use the given information to provide the desired estimate. If necessary, enter the answer to the nearest hundredth.

Answer 1

Tom-------------- >10 sq ft per minute

Tim------------------- >3.5*10=35 sq ft per minute

Both painters (10+35)=45 sq ft per minute

let's assume a cubic unit crate----------> V1=1*1*1=1 feet3

the total surface of the cube is S1=6*(1*1)=6 sq ft

if the volume of the cube increases twice

V2=2 feet3 ------------------- > 2=x*x*x------------- >x=2^(1/3)

And the S2=6*(2^(1/3)* 2^(1/3)=9.5244 sq ft

V2/V1=9.5244/6=1.5874

Therefore

If Tim and Tom----------------------- > take 1 day----------- > to paint a crate V1

For the crate V2------------- > take 1.5874 days

assuming an 8-hour work day

0.5874*8=4.70 hr-------------- > 4 h 42 min

The answer is 1 day 4h 42 min