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Add their rates of mowing to get the rate mowing together
Jack's rate: 1 lawn/5 hrs
Marilyn's rate: 1 lawn/4 hrs
Rate working together = 1 lawn/x hrs

multiply both sides by


hrs
This is about 2 hrs and 13 min

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logs are exponents. This equation says that the
exponent with the base gives me
I can write it this way:

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Let = bill before tax


is the cost before tax

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The area, is the length x height
The line connecting (-3,-1) and (5,-1) is a horizontal line segment
with length and is unit below the x-axis
The other pair, (-1,4) and (7,4) also has a length
and also is horizontal with a height above the x-axis of
The total distance between the horizontal line segments is

square units

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Let = the speed of the other car.
Since they travel in opposite directions,
I can consider Hillary's car to be stationary
and the other car to be traveling at the sum
of their speeds, which is
First the nose of the other car has to travel 15 ft
to get side-by-side, and another 15 ft to get
past Hillary's car.
(there are 3600 sec /hour and 5280 ft/mile)




The other car's speed is 42.6 mi/hr

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Regrouping the units, I have
(ft/ft) x (s/s) , leaving mi/hr
Doing the calculation:

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If the ratio of the lengths is 3 to 1, the ratios of
the lengths to the total length is
3 to 4 and 1 to 4
given:
total length = in
shorter piece = in
-------------------

multiply both sides by

Since the total length is , the longer
piece is in

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Let = number of 200 lb orders for chemicals
Let = total dollar amount of order

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There must be a little more information. Is this problem
part of exercises on linear equations? If so,
given:
Let t represent the number of years since 1994.
(1994)
(2001)


Assuming this is a linear relation between and ,
The formula to use is:

plugging in data:





With this equation, you can find for any

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given:



By subtraction:




200 grams of the 25% copper and 800 grams
of the 50% copper should be used

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given:
mi/hr
mi
hrs
Going upstream:


Going downstream:


By substitution:






The speed of the current is 2 mi/hr
check answer:
Going upstream:



hrs
Going downstream:


hrs
hrs total
OK

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If they are cycling towards each other, you can think of one as
being stationary, and the other as moving at the sum of their speeds.
Thinking of the faster one as the one in motion, the equation is





The faster cyclist's speed is 27 mi/hr
check:
The slower cyclist:

mi
The faster cyclist:

mi

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">" means "greater than"

You know this is true
Just like an equaliy, you can add or
subtract the same number from
both sides, and it's still true.

I can rewrite this as:

You have to picture this on the number line.
I can rewrite again as:
(with many, many more 6's)
This is still true if you plot it on the number line.
Always make use of the number line whenever
you are confused by inequalities.

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You can break up 2 1/3 into a whole number, 2
and a fraction, 1/3.
Since there are 60 min in an hour, there are 120 min in 2 hrs
And 1/3 of an hour is 1/3 of 60 min, and that is 20 min
so the answer is 120 + 20 = 140 min in 2 1/3 hrs

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In min, the 1st car travels


mi
Assume you have a stopwatch and you start it
when the 2nd car enters the freeway.
Write equations for both cars that show
as the distance that the 2nd car goes
in order to catch the 1st car.
1st car:
(1)
(1)
2nd car:
(2)
Note that the time is when you stop the stopwatch
Set (1) = (2)


hr
It will take 2 hrs and 12 min for 2nd to catch 1st
check:
(1)
(1)

mi
and
(2)
(2)
mi
OK

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After gallons have been pumped from the
available gallons, this is
per cent of available gasoline

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The circumference, C, =
given: ft
ft
The angle formed at 2 o'clock is
of a whole circle- this is (10 min)/(60 min)

This is about 3.14159/6 feet

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Let = liters of pure acid needed
In words:
(total liters of acid)/(total liters of solution) = 20%
given:
acid already in solution: liters
-------------



liters
1.25 liters of acid are needed
check:





OK

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Let = length of shortest piece
given:




The shortest piece is 5 ft long

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When the ball hits the ground, , so


Divide both sies by

Use quadratic equation to find







Take the negative square root in order
to get a positive answer:


sec
The ball will hit the ground in 5 sec
check answer:




OK

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In words:
(ml of salt)/(total ml of solution) = % salt
given:
Total ml of solution: ml
Salt in solution: ml
= .54%

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Let = kg of 11 rs/kg rice needed
Let = kg of 2 rs/kg rice needed
= cost of 11 rs/kg rice
= cost of 2 rs/kg rice
= cost of 7 rs/kg rice
given:
(1)

(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)


The quantity of 11 rs/kg rice needed is 95 kg
And, from (1):



check answer:
(2)
(2)


OK

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Let =number of items that she sold for a nickel
Then = number of items that she sold for a dime
given:






She sold 5 items for a nickel and 7 items for a dime
check:





OK

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You can't buy 100 cows, because 100 x $10 = $1,000
50 cows is still too much, since 50 x $10 = $500
since 10 cows cost 10 x $10 = $100, you must spend less than that
Suppose you buy 9 cows, then 9 x $10 = $90
There is $10 left
If you bought all hens to get 100 animals, that would make
80 hens = 80 x 1/8 = $10, and $90 + $10 = $100, but
there are only 9 + 80 = 89 animals
----------------------------
Suppose you buy 8 cows, then 8 x $10 = $80
then 160 hens = 160 x 1/8 = $20, that's 168 animals
If you buy 72 hens, then 72 x 1/8 = $9
There is $11 left to buy 11 sheep, but 8 + 72 + 11 = 91
----------------------------
If you buy 8 cows and 80 hens, that's 80 x 1/8 = $10
$10 + $80 = $90 , you have $10 to buy 10 sheep, and that's
8 + 80 + 10 = 98 animals
----------------------------
If you buy 8 cows and 88 hens that's 88 x 1/8 = $11
$11 + $80 = $91 You have $9 left to buy 9 sheep, and that's
8 + 88 + 9 = 105 animals
-----------------------------
It looks like you can't do it with 8 cows, and I'd guess that
7 cows would work
7 cows = $70
80 hens = $10
13 sheep = $13
$70 + $10 + $13 = $93
----------------------
7 cows = $70
72 hens = $9
21 sheep = $21
$70 + $9 + $21 = $100
That's 100 animals for $100

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In words:
(amount of salt in final solution)/(total gallons of final solution)
=45%
Let = gallons of 40% solution
Let = gallons of 60% solution
given:
Amount of salt in 40% solution =
Amount of salt in 60% solution =
(1)
(2)
(2)
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
(2)
(1)

gallons
And, from (1)



75 gallons of 40% solution and 25 gallons of 60% solution must be used
check answer:





OK

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Let = length of the planned trip in miles
The 1st day he hiked miles
The remaining distance is miles
On the 3rd day, he hiked half of that, or
miles
So far he has hiked miles
There are miles left
On the 4th day, he hiked miles
Reading carefully, the problem is telling me that
the 3 miles he traveled on day 4 was 1/5 of the
miles left , so


miles is the length of the planned trip
---------------------
Now, going back over the problem:
The 1st day he hiked miles
On the 3rd day, he hiked half of that, or
miles
So far he has hiked miles
and there are miles left
On the 4th day he hiked miles which is
of the miles left, or
So, he hiked of the
mile planned trip

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The equation of motion is:

given:

mi/hr
In hrs he travels

mi

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given:
(1)
(2) (in cents)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)


And, from (1),
(1)


She has 40 dimes and 44 quarters
check answer:
(2)
(2)


OK

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Let = number of pages in 1st book
= total pages in both books
= number of pages in 2nd book
given:

Multiply both sides by





The books have 900 pages and 1500 pages

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Let = speed of plane in still air
Let = wind speed
Against the wind:

With the wind:

(1)
(2)
Multiply both sides of (1) by and
multiply both sides of (2) by
(1)
(2)
Add the equations

km/hr
Plug this back into (1)
(1)


km/hr
check:
(2)


OK