Section 7.4 Homework Solution

Section 7.4 Homework and Math 6A problems Suggestion: Do the Math 6A problems first. Math 6A, Problem 7 on page 81 If Daniel took 2 hours to drive from Town A to Town B at 60 km/hr, then he drove a total distance of 60 km/hr × 2 hr = 120 km. The formula, Distance = Rate × Time may be rewritten as Time = Distance / Rate. Using this, and letting T be the time in hours for the trip at 80 km/hr, we get T = 120 km / (80 km/hr) = 120/80 hr = 3/2 hr = 1 hour and 30 minutes. Math 6A, Problem 2 on page 82 a) Distance = 10 km/hr × 2 hr = 20 km. b) His increased average speed is 12 km/hr. So the time for the trip at this speed is 20 km/(12 km/hr) = 20/12 hr = 5/3 hr = 1 hour and 40 minutes. Section 7.4 Problems 4. ! 1.9 liter liter 1 gal 60 sec = 1.9 × × sec sec 3.8 liter 1 min ! 1 60 liter gal sec gal = (1.9 × × ) × × = 30 3.8 1 sec liter min min ! ! ! ! gal . Note how the units cancel as if they were numbers and note also min ! ! ! ! ! ! 1 gal 60 that is another name for 1 because 1 gallon is the same as 3.8 liters, and 3.8 liter 1 sec is ! another name for 1 because 60 seconds is the same as 1 minute. min The answer is 30 ! ! ! 5. 0.3 liters/ meter2 / day × 7 days/week × 6000 meter2 = (0.3 × 7 × 6000) liters/week = 12,600 liters/week ! 6. The answer is c) 48 mph. Here is the solution: Average speed is the total distance traveld divided by the time it took. Let D be the distance between City A and City B. And let T be the time it took to travel from City A to City B at a speed of 60 mph. Then D/T = 60 mph. Since T is the time it took to go from City A to City B at 60 mph, 3T/2 is the time for the return trip at the speed of 40 mph. The total distance for the round trip is 2D. The total time for the round trip is T + 3T/2 = 5T/2. The average speed (distance over time) is 2D/(5T/2) = 4/5 × D/T = 4/5 × 60 mph = 48 mph. 7. Let "job" mean filling the swimming pool. 1 job The first hose fills the pool at a rate of . 30 hour 1 job The second hose fills the pool at a rate of . 70 hour ! ! 1 1 job 1 job Together they fill the pool at a rate of ( + ) = . So the job is 30 70 hour 21 hour ! ! is 21 hours. completed after 21 hours. The answer ! ! ! 50 pounds ! ! 8. The first corn mill grinds corn at a rate of . 6 min 50 pounds The second corn mill grinds corn at a rate of . 9 min ! ! 50 50 pounds 125 pounds Together they grind corn at a rate of ( + ) = . 6 9 min 9 min ! ! If T is the number of minutes required to grind 1500 pounds of corn, then ! ! ! ! ! 125 pounds 125 pounds × T min = 1500 pounds. So, T min = 1500 pounds ÷ = 9 min 9 min ! ! 1500 pounds × ! ! min 9 = 108 min. The answer is 108 ! minutes. ! 125 pounds