ALGEBRA WORD PROBLEMS FOR CLASS 6

Problem 1 :

Mrs. Saunders can clean the windows of her house in 3 hours. Her daughter can clean the windows in 6 hours. How long will it take them to clean the windows if they work together?

Solution:

Saunders = 1/3 windows per hours

Daughter = 1/6 windows per hours

Working together, they clean

It will take them 2 hours to finish when they work together.

Problem 2 :

A driver can deliver his newspapers in 80 minutes. His friend can take care of the same route in 2 hours. How long would it take them to do the job together?

Solution:

The driver's ratio is of 1/80

His friend's ratio is of 1/120

The together ratio is of 1/x

It would take them 48 minutes to do the job together.

Problem 3 :

One pipe can fill a tank in 8 minutes, a second can fill it in 12 minutes and a third can fill it in 24 minutes. If the tank is empty how long will it take the three pipes, operating together, to fill it?

Solution:

The rate of the first pipe = 1/8

The rate of the second pipe = 1/12

The rate of the third pipe = 1/24

Problem 4 :

Two printing presses, working together, can complete a job in 2 hours. If one press requires 6 hours to do the job alone, how many hours would the second press need to complete the job alone?

Solution:

First press = 1/6 hours

Second press = 1/x hours

working together = 1/2 hours

So, second printing press needs 3 hours by itself.

Problem 5 :

One supplementary angle is 5 more than six times the other angle. What is the measure of each angle? 

Solution:

Let one angle = x

other angle = y

x + y = 180° ---> (1)

x - 5 = 6y

x - 6y = 5 ---> (2)

Substitute equation (2) from (1),

x - x + y + 6y = 180 - 5

7y = 175

y = 25°

Put y = 25° in equation (1)

x + y = 180°

x + 25° = 180°

x = 180 - 25

x= 155°

So, one angle = 155°

and other angle = 25°

Problem 6 :

One complementary angles measures 18 less than five times the other angle. What is the measure of each angle?

Solution:

Let one angle = x

Other angle = 5x - 18

x + (5x - 18) = 90°

6x - 18 = 90°

6x = 108

x = 108/6

x = 18

So, one angle = 18°

Other angle = 5(18) - 18

= 90 - 18

= 72°

Problem 7 :

If the perimeter of an equilateral triangle is 24 inches, find a side of the triangle.

Solution:

Perimeter of an equilateral triangle = 3a

24 = 3a

a = 24/3

a = 8 in

Problem 8 :

Each of the equal sides of an isosceles triangle is 4 times the third side. The perimeter of the triangle is 144 inches. Find the sides of the triangle.

Solution:

Let the third side be x.

Each of the equal side is 4x.

Perimeter = 144 in

P = x + 4x + 4x

P = 9x

144 = 5x

x = 16 in

Second side = 4x = 4(16)

= 64 in

Third side = 4x = 4(16)

= 64 in

The sides of the triangle are 16 in, 64 in and 64 in.

Problem 9 :

The perimeter of a triangle is 73 inches. If the second side is 5 inches longer than twice the first side, and the third side is 4 inches less than three times the first side, how long is each side?

Solution:

Let first side be x.

Second side = 2x + 5

Third side = 3x - 4

The sum of the length of the sides is equal to the perimeter.

x + 2x + 5 + 3x - 4 = 73

6x + 1 = 73

6x = 72

x = 72/6

x = 12 in

Second side = 2(12) + 5

= 29 in 

Third side = 3(12) - 4

= 32 in

Problem 10 :

The length of a rectangle is three times the difference of the width and two. If the perimeter of the rectangle is 60 cm, what is the length of the rectangle?

Solution:

Let the width be x.

Length = 3(x - 2)

Perimeter of rectangle = 60 cm

Perimeter = 2(length + width)

2(3(x - 2) + x)) = 60

2(3x - 6 + x) = 60

2(4x - 6) = 60

8x - 12 = 60

8x = 72

x = 9 cm

Length = 3(x - 2)

= 3(9 - 2)

= 3(7)

Length = 21 cm

So, width = 9 cm

Length = 21 cm

Problem 11 :

A rectangular playground is enclosed by 440 feet of fencing. If the length of the playground is 20 feet less than 3 times the width, find the dimensions of the playground.

Solution:

Let the width be x feet

The length = 3x - 20 feet

2(x + 3x - 20) = 440

2(4x - 20) = 440

8x - 40 = 440

8x = 480

x = 480/8

x = 60 feet

Length = 3(60) - 20

= 180 - 20

= 160 feet

So, width = 60 feet

Length = 160 feet.