CST 15, 21, 23B

CA Standard 15.0 Students apply algebraic techniques to solve rate, work, and mixture problems.

Ex 1: Joe wants to change the coolant mixture in his truck to 60% coolant. Right now his cooling system has 4 quarts which is 50% coolant. How much pure coolant does he need to add to accomplish this? 50% 100% 60% mix + = x 100x 60 x+460x mix

x = 60x % 100% 60% mix + = A=amountP=percent x 100x 60 x+460x + 240

x = 60x x = x = 40 x = 1qt

Ex 2: 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

hrs

rate 1 st 2 nd 50 r r = = 60x5 =300 2r = 150 r = 75 mph Ex 3: John averages 60 mi/hr during a 5 hour trip. If he averages 50 mi/hr during the first 3 hours, what must his average speed be during the last 2 hours?

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

hrs

Ex 5: If train A and train B leave the same station at the same time travelling in opposite directions, how long will it take for them to be 385 miles apart if train A is going 50 mi/hr and train B is going 60 mi/hr? t5050t t 60 60t t = 385 t = 3.5 hrs D = r x t rate

Ex 6: A chemist has 40 mL solution that is 50% acid. How much water should be added to the original solution to make a solution that is 10% acid? 50% 0% 10% + = x 0 10 x+4010x mix

2000 = 10x % 0% 10% + = x 0 10 x+4010x + 400

2000 = 10x = 10x 160mL = x