Irian can bar code the books in 15 hours. Viri can do the job in 12 hours. If they work together, how long will it take for them to barcode the books?

x 15 + x 12 = 1 I alone Time together V alone Whole job

Pump A can unload the oil in 30 h and pump B can unload it in 24h. How long does it take to unload the oil if both work together?

Pump A can unload the oil in 60 h. When pump A and pump B were used together, they were able to unload the oil in 15h. How long does it take for pump B to unload the oil by itself?

An old conveyor takes 21 h to move the coal output. A new conveyor can do it in 15h. How long does it take to move the coal if 2 old conveyors and one new one were used?

Pipe A can fill a storage tank in 24 h. When both pipes A & B were used, the job was done in 6 h. How long does it take pipe B to fill the storage tank alone?

A pipe can fill a storage tank in 24 h if the drain is closed. A drain can empty the tank in 60 h if the pipe is closed. How long does it take to fill the tank if the pipe and the drain are both open?

One machine can pave a mile of highway in 10 h. An older machine can pave a mile of highway in 18 h. If both are used, how long does it take to pave 1 mile of highway? 20 miles of highway?

Yellow packet pg 24B

Yellow packet pg 25 D #1

20lbs $3/lb ? lbs $5/lb ? lbs $3.50 /lb Total$ x y 60 5x 3.5y + = + = lbs$

Yellow packet pg 25 D #2

? lbs $7/lb 14 lbs $4/lb ? lbs $5/lb Total$ + = + = lbs$ x y 7x 56 5Y

Do you know how investments work? Amount invested: $1000 Interest Rate: 6% Interest earned?

I have $2000. I invest part of it in an account earning 5% and the other part earning 2%. If at the end of the year, my total interest earnings was $64, how much invested in each?

$ Interest x $ x 0.02y 64 + = + = $ Invest% 5% y 2%

I invest some $ in an account earning 5% and I invest twice that amount in a 2% account. If at the end of the year, I earned $90 interest, how much was invested in each?

$ Interest x0.05x 0.02(2x) 90 + = $ Invest% 5% 2x2%

Ana invests $200 more in a 4% account than in a 5% account. At the end of the year, she receives the same amount of interest from both. How much was invested in each?

$ Interest x0.05x 0.04(x+200) = $ Invest% 5% x %

Continue Yellow Packet pg 25 C 6 – 13 and D all

Rate Time Distance How fast you’re traveling Rate of speed mph, kph, k/hr m/sec, ft/min miles, km, m, ft Hours, minutes, seconds

What is the equation that connects Rate, Time, & Distance? D = RT

Diana and Jaime start from the same point at the same time and travel in opposite directions on their bikes. If Diana travels at 8mph & Jaime at 7mph, in how many hours will they be 45 mi apart?

45 miles

RTD 8 7 t t = 8 t 7 t 8 t + 7 t = 45

How do we translate: Monica went to San Diego and came back. The whole trip took 6 hours. go back t 6 - t

Sonia drives her car at 25 mph to the bus stop where she takes a bus that goes 50 mph. If her total trip was 175 miles and took 4 hours how long was she on the bus?

RTD = 25 t 50(4 – t ) 25t + 50(4 – t) = 175 t 4 - t

How do we translate: Angel leaves 6 hours later than Marcie AMAM t t - 6 t t + 6

A train leaves the station & travels south at 60 mph. Two hours later, another train leaves the station and travels south at 65 mph. How many hrs will the 1 st train have traveled when the 2 nd overtakes it?

RTD t t - 2 = 60t 65(t – 2) 60t = 65(t – 2)

Yellow packet pg 24 A #1

Ontario airport

4000 km

RTD t t = 850 t 750 t 850 t t = 4000

Yellow packet pg 24 #2

20 km

RTD x + 6 x 0.5 =.5(x+6).5x.5(x+6) +.5x = 20 J E

Yellow packet pg 24 #3

Ontario Fresno

Ontario Fresno

RTD t t = 60(t+1.5) 80t 60(t + 1.5) = 80t go return

Continue with pg 24A #

Direct Variation: Your pay, P, varies directly with the number of hours, H, you work. The more you work, the more you get paid. P = k H

In this case, k represents your hourly wages P = k H

Instead of saying: P varies directly with H, we can also say: P is directly proportional to H. P = k H P is some number times H

Inverse Variation: Suppose you have to drive 400 miles to San Francisco. Your speed, S, and the number of hours, T, it will take to get there vary inversely.

The faster you drive, the less time it will take to get there. More speed means less time. S = k / T

In this case, k represents the total number of miles you travelled S = k / T

Instead of saying: S varies inversely with T, we can also say: S is inversely proportional to T. S = k / T S is 400 / T

Direct variation Inverse variation Joint variation Variation y varies directly with x: y = kx y varies inversely with x: y = k / x y varies jointly with x & z: y = kxz

Direct variation Inverse variation Variation y is directly proportional to x: y = kx y is inversely proportional to x: y = k / x

x and y vary directly. If x is 3 when y is 9, write an equation that relates the variables. Find x when y = 15.

x and y vary inversely. If x is 3 when y is 9, write an equation that relates the variables. Find x when y is 15.

D and T are directly proportional. If D is 3 when T is 9, write an equation that relates the variables. Find T when D is 9.

V and t are inversely proportional. If V is 19.6 when t is 2, write an equation that relates the variables. Find V when t is 4.

Area is directly proportional to the square of the radius. If the area is 78.5 when the radius is 5, write an equation that relates the variables.

x varies jointly with y and z. If x is 30 when y is 9 and z is 5, write an equation that relates the variables.

V varies inversely with the square of r. If V is 7 when r is 2, find V when r = 3.

T is directly proportional to the square root of a. When a = 9, T = 18. Find a if T = 24.

Temperature of a gas varies jointly with volume and pressure. If the temp of a gas is 294 degrees when the volume is 8000 and pressure 0.75, find the temp when V = 7000 and P = 0.87

The intensity, I, of sound (watt/m 2 ) varies inversely with the square of the distance d (m) from a sound source. At dist of 1 m from a stage, intensity of a rock concert is 10 w/m 2. At 10 m, find I

The heat loss, h (watts), through a glass window varies jointly with the window’s area, A (m 2 ), and the difference between inside and outside temp, d (kelvins)

A window with area 1 m 2 and a temp difference of 1 kelvin has a heat loss of 5.7 watts. What’s the heat loss through a window with area 2.5 m 2 and a temp difference of 20 kelvins?