Kellie can mow the campus yard in 2 ½ hours. When Bobby helps, they can mow the yard in 1 ½ hours. How long would Bobby need to mow the yard by himself?
Let t represent the number of hours Bobby needs to mow the yard himself. Kellie’s time is 2 ½ or 5/2.
Then her rate is
.
The together
time is 1 ½ or 3/2, so the together rate is 
.
The equation
to solve is 2/5 + 1/t = 2/3. The LCD is 15t.
Bobby needs
15/4 = 3 ¾ hours or 3
hours 45 minutes to mow the yard by himself.
Practice
1. Sherry
and Denise together can mow a yard in 20 minutes. Alone, Denise can mow the
yard in 30 minutes. How long would Sherry need to mow the yard by herself?
2. Together,
Ben and Brandon can split a pile of wood in 2 hours. If Ben could split the
same pile of wood in 3 hours, how long would it take Brandon to split the pile
alone?
3. A
boy can weed the family garden in 90 minutes. His sister can weed it in 60
minutes. How long will they need to weed the garden if they work together?
4. Robert
needs 40 minutes to assemble a bookcase. Paul needs 20 minutes to assemble the
same bookcase. How long will it take them to assemble the bookcase if they work
together?
5. Together,
two pipes can fill a reservoir in ¾ of an hour. Pipe I needs one hour ten minutes (1 ⅙ hours) to
fill the reservoir by itself. How long would Pipe II need to fill the reservoir
by itself?
6. A
pipe can drain a reservoir in 6 hours 30 minutes (6 ½ hours). A larger pipe can
drain the same reservoir in 4 hours 20 minute (4 ⅓ hours). How long will it
take to drain the reservoir if both pipes are used?
Solutions
In the
following, t will represent the unknown time.
1.
The
equation to solve is 1/t + 1/30 = 1/20. The LCD is 60t.
Alone,
Denise can mow the yard in 60 minutes.
2.
The
equation to solve is 1/3 + 1/t = 1/2. The LCD is 6t.
Brandon
can split the wood-pile by himself in 6 hours.
3.
The
equation to solve is 1/90 + 1/60 = 1/t. The LCD is 180t.
Working together, the boy and girl need 36 minutes to weed the garden.
4.
The equation to solve is 1/40 + 1/20 = 1/t. The LCD is 40t.
Together Robert and Paul can assemble the bookcase in 13⅓ minutes or 13
minutes 20 seconds.
5.
The equation to solve is 6/7 + 1/t = 4/3. The LCD is 21t.
Alone, Pipe II can fill the reservoir in 2 1/10 hours
or 2 hours, 6 minutes. (1/10 of an hour is 1/10
of 60 minutes and 1/10 · 60 = 6.)
6.
The equation to solve is 2/13 + 3/13 = 1/t. The LCD is 13t.
Together
the pipes can drain the reservoir in 2⅗ hours or 2 hours 36 minutes. (⅗ of hour
is ⅗ of 60 minutes and ⅗ · 60 = 36.)
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