Solutions to Equation Worksheet: Draining Fluid, Distance Traveled, and Walking Speeds - P, Assignments of Algebra

Download Solutions to Equation Worksheet: Draining Fluid, Distance Traveled, and Walking Speeds - P and more Assignments Algebra in PDF only on Docsity! Solutions to Equation Application Worksheet 1. This is very similar to Example 5 on page 94 (which you should have read). If x is the amount of fluid we drain and replace with pure antifreeze, we have: (25% of (10− x) quarts) + (100% of x quarts) = (40% of 10 quarts) . .25(10− x) + x = .4(10) 2.5− .25x + x = 4 .75x = 1.5 x = 2. (1) So, Linnea should drain 2 quarts from the radiator and pour in 2 quarts of antifreeze. 2. This is very similar to Example 6 on p. 95. If r is the speed during the first direction, and t is the time spent going the first direction, then using distance = rate× time, we have: (rate 1st dir.) (time 1st dir.) + (rate 2nd dir.) (time 2nd dir.) = total distance 160 = rt + (r − 10)(3.6− t) 160 = rt− rt + 3.6r + 10t− 36 160 = 3.6r + 10t− 36 196− 3.6r = 10t 19.6− .36r = t (2) We also know that rt = 80, so we have: 80 = rt 80 = (19.6− .36r)r 80 = 19.6r − .36r2 .36r2 − 19.6r + 80 = 0 36r2 − 1960r + 8000 = 0 (3) Applying the quadratic formula, we get r = 50 or r = 40/9. However, the second solution makes no sense, as it would require the Sarah to drive 40/9−10 < 0 mph the second direction. So, we have r = 50 mph, and t = 19.6 − .36r = 1.6 hours. So, Sarah drives to Portland at 50 mph for 1.6 hours, and back at 40 mph for 2 hours. You can substitute this back into the original equation to check that it is correct. 3. If r is the rate of the person walking down 11th, using the Pythagorean Theorem, we have: 502 = (20r)2 + (20(r − .5))2 2500 = 400r2 + 400(r2 − r + .25) 2500 = 400r2 + 400r2 − 400r + 100 0 = 800r2 − 400r − 2400 (4) Applying the quadratic formula, we have r = −1.5 or r = 2. The only answer that makes sense is r = 2. We can substitute back into the original equation to check. So, one person walks down 11th at 2 m/s while the other walks down Willamette at 1.5 m/s. 1