Question 212049
brandon can shovel his sidewalk in 8 minutes nad his brother can shovel the sidewalk in 12 minutes.  if they work together, how long will it take them to shovel the sidewalk?


Since Brandon can shovel the sidewalk in 8 minutes, in 1 minute, he will have shoveled {{{1/8}}} of the sidewalk


Since his brother can shovel the sidewalk in 12 minutes, in 1 minute, he will have shoveled {{{1/12}}} of the sidewalk


Let the time that both will take to shovel the sidewalk be B


We can then set up the proportion to determine the value of B, in munutes


{{{((1/8) + (1/12))/1 = 1/B}}}

{{{((3 + 2)/24)/1 = 1/B}}}

{{{(5B/24) = 1}}} ------> Cross-multiplying


5B = 24


{{{B = 24/5}}} = {{{highlight_green(4.8)}}} minutes for both to shovel the sidewalk