Algebra Demystified 2nd Ed

272 algebra De mystif ieD

There are four equations in this chart. One of them is the one we use to

solve for the unknown. Each horizontal line in the chart represents the equa-

tion Q = rt for that particular line. The fourth equation comes from the sum

of each worker’s rate equaling the together rate. Often, the fourth equation

is the one we need to solve. Remember, as in all word problems, all units of

measure must be consistent.

EXAMPLE

Joe takes 45 minutes to mow a lawn. His older brother Jerry takes 30 min-

utes to mow the lawn. If they work together, how long will it take for them

to mow the lawn?

The quantity in each of the three cases is 1—there is one yard to be mowed.

Use the formula Q = rt and the data given in the problem to fill in all nine

boxes. Because we are looking for the time (in minutes) it takes for them to

mow the lawn together, let t represent the number of minutes needed to

mow the lawn together.

Worker Quantity Rate Time

Joe 1 45

Jerry 1 30

Together 1 t

Because Q = rt, r = Q

t

. But Q = 1, so r =

1

t. This makes Joe’s rate

451 and Jerry’s

rate 301. The together rate is

1

t.

Worker Quantity Rate Time

Joe 1 1/45 45

Jerry 1 1/30 30

Together 1 1/t t

Of the four equations on the chart, only “Joe’s rate + Jerry’s rate = Together

rate” has enough information in it to solve for t.

EXAMPLE

Joe takes 45 minutes to mow a lawn. His older brother Jerry takes 30 min-