If Michael can paint a house in 8 hours and a Samantha can paint a house in 2
hours, how long will it take them together?
You can do it in your head without algebra, but you're probably supposed
to do it by algebra, so we''l do it both ways. First, in your head:
In the 8 hours Michael takes to paint only one house, Samantha will have
painted 4 houses. So in 8 hours together they will have painted 5 houses. So
it'll only take them 1/5th of 8 hours to paint just one house, and 1/5 of 8 is
8/5 hours. That's 1 3/5 hours or 1 hour and 36 minutes.
Now we do it using algebra:
Make this chart:
Houses painted Time in hours Rate in houses/hour
Michael
Samantha
Together
Let x be the time it takes them to paint 1 house working together, so
fill in 1 for the number of houses, and x for the time.
Houses painted Time in hours Rate in houses/hour
Michael
Samantha
Together 1 x
>>...Michael can paint ONE house in 8 hours...<<
So we fill in 1 for his number of houses painted and 8 for his time:
Houses painted Time in hours Rate in houses/hour
Michael 1 8 1/8
Samantha
Together 1 x 1/x
>>...Samantha can paint a house in 2 hours...<<
So we fill in 1 for her number of houses painted and 2 for her time:
Houses painted Time in hours Rate in houses/hour
Michael 1 8
Samantha 1 2
Together 1 x
Now we fill the rate in houses/hour by dividing houses painted by hours
in all three cases:
Houses painted Time in hours Rate in houses/hour
Michael 1 8 1/8
Samantha 1 2 1/2
Together 1 x 1/x
Now we form our equation from the rates:
Michael's rate + Samantha's rate = their rate together
1/8 + 1/2 = 1/x
Multiply through by the LCD of 8x
x + 4x = 8
5x = 8
x = 8/5
x = 1 3/5 hours or 1 hour 36 minutes.
Edwin