How long will it take them to clean the house if they work together? Pete can mow and clean up a lawn in 8 hours. If Sally helps, the Job can be done in 6 hours. How long would it take Sally, working alone, to do the Job? Math 070 chanter / Rational Expressions Ana Equators ( A new printer can print checks three times faster than an old printer. The old printer can print the checks in 30 min. How long would it take to print the checks when both printers are operating? Tim can put a new roof on a house twice as fast as Mark.

Working together they can roof a house in 4 days. How long would it take Tim to roof the house if he worked alone? 31 Math 070 Chapter 7 Rational Expressions and Equations (7. 6) Distance Problems (if time is the same in both situations) Use the formula: 5. 1st didst. 2nd didst. 0 1st rate 2nd rate The speed of a freight train is 30 MPH slower than the speed of a passenger train. The freight train travels 140 mi in the same time that it takes the passenger train to travel 210 mi. Find the speed of each train.

A train travels 100 mi in the same time that a light plane can fly 260 mi. If the speed of the plane is 80 MPH faster than that of the train, find the rate of each. 32 Math 070 Chapter 7 Rational Expressions and Equations (7. 6) A boat can travel 100 mi downstream in the same time that it takes to travel 60 mi upstream. The speed of the current in the stream is 8 MPH. Find the speed of the boat in still water. An airplane flies 1500 mi with the wind. In the same amount of time, it can fly 1260 mi against the wind. The speed of the plane in still air is 230 MPH.

Find the speed of the wind. 33 Matt 0/0 chanter / Rotational Expressions Ana Equators ( The formula for this last one is different because the times are not the same but the total time is given. Use A boat moves at 16 MPH in still water. It travels 30 miles upstream and then 30 miles downstream in a total of 4 hours. What is the speed of the current? MATH-070 Rational Formulas Use the same strategy as when solving rational equations. Solve E 10 f for f. 1110 OPAC for c. 35 non Formulas ex. cow for z. For D. 111 poops for p. Sec. 7. Variation Direct Variation (when one thing goes up, so does the other) General format: 1 . Yoke The distance an object falls (from rest) varies directly as the square of the time it falls. If an object falls 784 Ft in 7 sec, how far will it fall in 10 sec? I nee welling AT an deject on ten moon varies alertly as Its welling on earth A person who weighs 147 lbs on the earth weighs 24. 5 lb on the moon. How much would a 186- lb person weigh on the moon? 37 sec 7. 8 Inverse Variation (When one thing goes up, the other does k you down. General format: x 3. The volume of a gas varies inversely as the pressure on it. The volume of a gas is 160 CM under a pressure of 40 keg/CM. What will be its volume under a pressure of 32 keg/CM? The time required to empty a tank varies inversely as the rate of pumping. A pump can empty a tank in 80 min at a rate of 1200 Min. How long will it take the pump to empty the tank at a rate of 2000 L/min? Joint Variation (More than two things involved! ) 5. The area of a trapezoid is Jointly proportional to its height and the sum of its two bases.

If the area is 60. 2 CM when the height is 8. 6 CM and the two bases measure 4. 2 CM and 9. 8 CM, find the area when the height is 6. 5 CM, and the two bases measure 3. 4 CM and 4. 6 CM. The height of a right cylindrical cone is directly proportional to the its volume and inversely proportional to the area of its base.