Algebra 1 Common Core Student Edition, Grade 8-9

To solve a w ork problem , find th e fraction of th e job each p erso n does in one u n it of

tim e (for example, in 1 h or 1 m in). The sum of th e fractions for everyone w orking is the

fraction of th e job com p leted in one u n it of time.

Solving a W ork Problem

Painting Amy can paint a loft apartment in 7 h. Jeremy can paint a loft apartment of

the same size in 9 h. If they work together, how long will it take them to paint a third

loft apartment of the same size?

• Amy's painting time is 7 h.


• Jeremy's painting time is 9 h.

Amy and Jeremy's

combined painting

time

Find w hat fraction of a loft each

person can paint in 1 h. Then write

and solve a rational equation.

Think
Where have you seen
a problem like this
before?
In Problem 1 of this
lesson, you solved
a similar equation
containing rational
expressions.

Relate

fraction of loft Amy

can p ain t in 1 h

fraction of loft Jeremy

can p ain t in 1 h

fraction of loft

painted in 1 h

Define Let t = th e p ainting tim e, in hours, if Amy a n d Jerem y w ork together.

Write

63f I 7 + 9 631

+

97+ 7t= 63

16t= 63

M u ltip ly each side by the LCD, 63t.

Distributive Property

Simplify.

t = | | , o r 3 y | Divide each side by 16.

It will take Amy an d Jerem y ab o u t 4 h to p ain t the loft a p a rtm e n t together.

& G o t It? 3. O ne hose can fill a pool in 12 h. A nother hose can fill th e sam e pool in 8 h.

How long will it take for b o th hoses to fill th e pool together?

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