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Problems about Numbers

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5.6 – Applications. Problems about Numbers. If one more than three times a number is divided by the number, the result is four thirds. Find the number. LCD = 3x. Time to sort one batch (hours). Fraction of the job completed in one hour. 5.6 – Applications. Ryan. Mike. Together.

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slide1
5.6 – Applications

Problems about Numbers

If one more than three times a number is divided by the number, the result is four thirds. Find the number.

LCD = 3x

slide2
Time to sort one batch (hours)

Fraction of the job completed in one hour

5.6 – Applications

Ryan

Mike

Together

Problems about Work

Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort a batch in 3 hours. If they work together, how fast can they sort one batch?

2

3

x

slide3
Time to sort one batch (hours)

Fraction of the job completed in one hour

5.6 – Applications

Ryan

Mike

Together

Problems about Work

2

3

x

LCD =

6x

hrs.

slide4
Time to mow one acre (hours)

Fraction of the job completed in one hour

5.6 – Applications

James

Andy

Together

James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together?

2

8

x

slide5
Time to mow one acre (hours)

Fraction of the job completed in one hour

5.6 – Applications

James

Andy

Together

2

8

x

LCD:

8x

hrs.

slide6
Time to pump one basement (hours)

Fraction of the job completed in one hour

5.6 – Applications

1st pump

2nd pump

Together

A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone?

12

x

slide7
Time to pump one basement (hours)

Fraction of the job completed in one hour

5.6 – Applications

1st pump

2nd pump

Together

12

x

slide9
5.6 – Applications

Distance, Rate and Time Problems

If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive?

slide10
5.6 – Applications

A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles.

x

t

450 mi

t

x + 15

600 mi

slide11
5.6 – Applications

x

t

450 mi

t

x + 15

600 mi

LCD:

x(x + 15)

x(x + 15)

x(x + 15)

slide12
5.6 – Applications

x(x + 15)

x(x + 15)

Motorcycle

Car

slide13
5.6 – Applications

A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water?

boat speed = x

t

x - 5

22 mi

t

x + 5

42 mi

slide14
5.6 – Applications

boat speed = x

t

x - 5

22 mi

t

x + 5

42 mi

LCD:

(x – 5)(x + 5)

(x – 5)(x + 5)

(x – 5)(x + 5)

slide15
5.6 – Applications

(x – 5)(x + 5)

(x – 5)(x + 5)

Boat Speed

5 7 division of polynomials
5.7 – Division of Polynomials

Review of Long Division

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