10.7 HW Answers

1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12.

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17. 18. 19.

Scoring Your Homework Count how many problems you missed or didn’t do 0-1 missed = 10 2-3 missed = 9 4-5 missed = 8 6-7 missed = 7 8-9 missed = 6 10-11 missed = 5 12-13 missed = 4 14-15 missed = 3 16-17 missed = 2 18-19 missed = 1 20-21 missed = 0

Rate Problems

A rate is way of expressing how fast something occurs A rate is way of expressing how fast something occurs. For example, how long it takes to walk or run one mile, how far a car goes in one hour, how long a pump takes to fill a swimming pool, how long it takes a worker to paint a house, etc. Rates are usually expressed as some kind of event per unit of time: mi/hr (rate of speed), $/hr (rate of earning), cubic feet/sec (rate of pumping water)

Let's look closer at the speed of a car Let's look closer at the speed of a car. If the car is travelling at 30 miles each hour, we say its rate or speed is 30mi/hr. If it travels constantly at this speed for 10 hours, how far will it go? Clearly the time must be multiplied to the speed to get the distance travelled. Therefore:

We can use this formula to solve different kinds of problems involving rates. Use a chart to organize your information.

Ex 1: During a 456 mile trip, Lucy drove the first two hours at an average speed of 48 mi/hr. During the remainder of the trip, her friend Ethyl drove for another 8 hrs. What was Ethyl's average speed? Strategy to solve: 1) Write known amounts in table 2) Calculate any blanks possible 3) Use a variable for unknown amount 4) Write an equation using using two known quantities and only one variable

Ex 1: During a 456 mile trip, Lucy drove the first two hours at an average speed of 48 mi/hr. During the remainder of the trip, her friend Ethyl drove for another 8 hrs. What was Ethyl's average speed? distance = rate  time Lucy Ethyl 96 48 2  360 8 r  456

96 48 2 360 8 r 456 8r = 360 r = 45 mph distance = rate  time Lucy Ethyl 96 48 2  360 8 r  456 8r = 360 r = 45 mph

b) During a 840 mile flight, a small plane averages a speed of 160 mi/hr for the first 3 hours when one engine fails. For the remaining 3 hours of the flight, its speed was reduced to what average speed? distance = rate  time 480 160 3  1st 360 3 r 2nd  840

480 160 3 360 3 r 840 3r = 360 r = 120 mph distance = rate  time  2nd  840 3r = 360 r = 120 mph

Ex 2: Train A leaves the train station travelling at an average speed of 40 mi/hr. Eight hours later, Train B leaves in the same direction as Train A, but is travelling at an average speed of 60 mi/hr. How long will it be before Train B catches up to Train A?

In this table, your variable needs to represent the desired quantity, which is how long Train B travels until it catches up to Train A. For Train A's time, it has been travelling 8 hours longer than Train B, so represent this fact using an expression with "t". You will have two unknown distances, but what do you know about the two distances that each train will be from the station at the point where Train B catches up to Train A? Make your equation using this fact.

Ex 2: Train A leaves the train station travelling at an average speed of 40 mi/hr. Eight hours later, Train B leaves in the same direction as Train A, but is travelling at an average speed of 60 mi/hr. How long will it be before Train B catches up to Train A? distance = rate  time Train A Train B d 40 t  d t – 8 60 

distance = rate  time Train A Train B d 40 t  d 60 t – 8  60(t – 8) = 40t 60t – 480 = 40t 20t – 480 = 0 20t = 480 t = 24 hrs

Try: a) Rex Racer starts off around a go-cart track and is averaging a speed of 20 ft/s. His friend Sparky, starts 5 seconds later and averages 25 ft/s around the track. How long will it be before Sparky catches up to Rex? distance = rate  time d 20 t  Rex d t – 5 25 Sparky 

distance = rate  time d 20 t  Rex d t – 5 25 Sparky  25(t – 5) = 20t 25t – 125 = 20t 5t – 125 = 0 5t = 125 t = 25 sec

Work Problems Another type of rate is that at which work is done. Usually work is expressed as how much is done per unit of time: Cars painted per day, items assembled per hour, clay pots made per hour, lawns mowed per hour, bolts torqued per minute, etc. The total amount of work done clearly depends on how fast you work (rate) and how much time is spent on the task. Work done can be considered as 1 item done if it is something such as: one car painted, one house painted, one swimming pool filled by a pump, etc.

Ex 3: With spraying equipment, John can paint the wood trim on a small house in 8 hours. His assistant, Bart, must paint by hand since there is only one sprayer, and he needs 12 hours to complete the same type of job. If they work together on the same house, how long should it take them to complete the job? Since each worker will only do part of the job, their work is a fraction of the one job that will be completed. The work that they do then, must add up to one job.

Work = rate  time 1 8 John t  1 12 t Bart  1 house

hrs

Ex 4: A large water pump can fill a standard size swimming pool in 4 hours, while medium size water pump will take 6 hours to fill the same pool. Working both pumps at once, how long will it take to fill 3 standard size pools? Work = rate  time 1 4 large t  1 6 t  medium 3 pools

hrs

Try: c) Cletus can split a cord of wood in 4 days. His friend Gomer can split a cord in 2 days. How long would it take to split a cord of wood if they work together? Work = rate  time 1 4 Cletus t  1 2 t  Gomer 1 cord

days

d) Henry and Aaron own an oak wall-unit business d) Henry and Aaron own an oak wall-unit business. Henry can stain their large wall-unit in 3 hours and Aaron takes 4 hours. How long would it take them to stain 2 wall units if they work together? Work = rate  time 1 3 t Henry  1 4 t Aaron  2 walls

hrs

HW #1

1. Andy's average speed driving on a 4 hour trip was 45 mi/hr 1. Andy's average speed driving on a 4 hour trip was 45 mi/hr. During the first 3 hours he drove 40 mi/hr. What was his average speed for the last hour of the trip? distance = rate  time 120 40 3  1st 60 1 r 2nd  4  45 = 180

120 40 3 60 1 r 4  45 = 180 r = 60 mph distance = rate  time  1st 2nd  4  45 = 180 r = 60 mph