Question 1190679
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The owner works 4 times as fast as his assistant, so when working together he does 4/5 of the work.<br>
Working together, they take 32 minutes to do the job.<br>
So the owner does 4/5 of the job in 32 minutes and the assistant does 1/5.<br>
The owner does 4/5 of the job in 32 minutes, so the number of minutes it would take him to do the job alone is 32/(4/5) = 32*(5/4) = 40.<br>
The assistant does 1/5 of the job in 32 minutes, so the number of minutes it would take him to do the job alone is 32*5=160.<br>
ANSWERS:
owner 40 minutes
assistant 160 minutes<br>
Formally...<br>
x = minutes the owner takes to do the job
4x = minutes the assistant takes to do the job
32 = minutes it takes them together to do the job
1/x = fraction of the job the owner does in 1 minute
1/(4x) = fraction the assistant does in 1 minute
1/32 = fraction they do together in 1 minute<br>
{{{1/x+1/(4x)=1/32}}}<br>
multiply by 32x to clear fractions:<br>
{{{32+8=x}}}
{{{x=40}}}<br>
ANSWERS:
time for owner to do the job alone: x = 40 minutes
time for assistant to do the job alone: 4x = 160 minutes<br>