Linear Functions in Real-Life Contexts (Hard) Part 2 - SAT Math Practice Questions with Solutions

To find the linear function c(t), we first determine the rate of water consumption. The cyclist starts with 25 liters and has 10 liters left after 6 hours. The decrease in water volume is 25 - 10 = 15 liters over 6 hours, so the rate is \(\frac{15}{6} = 2.5\) liters per hour. The linear function is then c(t) = -2.5t + 25. One-third of the initial water supply is 25 / 3 ≈ 8.33 liters. Set c(t) = 8.33 and solve for t: -2.5t + 25 = 8.33 \Rightarrow t ≈ 6.67 hours. The y-intercept is 25, representing the initial volume of water the cyclist had before starting the cycling.

To find the linear function s(t), we first determine the rate of water consumption. The swimmer starts with 18 liters and has 10 liters left after 2 hours. The decrease in water volume is 18 - 10 = 8 liters over 2 hours, so the rate is \(\frac{8}{2} = 4\) liters per hour. The linear function is then s(t) = -4t + 18. Half of the initial water supply is 18 / 2 = 9 liters. Set s(t) = 9 and solve for t: -4t + 18 = 9 \Rightarrow t = 2.25 hours.

To find the linear function h(t), we first determine the rate of water consumption. The hiker starts with 20 liters and has 12 liters left after 4 hours. The decrease in water volume is 20 - 12 = 8 liters over 4 hours, so the rate is \(\frac{8}{4} = 2\) liters per hour. The linear function is then h(t) = -2t + 20. To find when the water runs out, set h(t) = 0 and solve for t: -2t + 20 = 0 \Rightarrow t = 10 hours.

To find the linear function g(t), we first determine the rate of water consumption. The cyclist starts with 15 liters and has 9 liters left after 3 hours. The decrease in water volume is 15 - 9 = 6 liters over 3 hours, so the rate is \(\frac{6}{3} = 2\) liters per hour. The linear function is then g(t) = -2t + 15. To find the volume after 5 hours, substitute t = 5 into the function: g(5) = -2(5) + 15 = 5 liters.

To find the linear function w(k), we first determine the rate of water consumption. The runner starts with 10 liters and has 7 liters left after 5 kilometers. The decrease in water volume is 10 - 7 = 3 liters over 5 kilometers, so the rate is \(\frac{3}{5}\) liters per kilometer. The linear function is then w(k) = -\frac{3}{5}k + 10. The y-intercept is 10, which represents the initial amount of water the runner had before starting the marathon.

In the function p(q) = -0.3q + 16, the y-intercept (where q = 0) represents the initial volume of sports drink the swimmer had before starting the training session. When q = 0, p(0) = 16, indicating that the swimmer started with 16 liters of sports drink.

In the function h(g) = -0.5g + 25, the y-intercept (where g = 0) represents the initial volume of water the hiker had before starting the trek. When g = 0, h(0) = 25, indicating that the hiker started with 25 liters of water.

In the function d(f) = -0.2f + 14, the y-intercept (where f = 0) represents the initial volume of energy drink the climber had before starting the ascent. When f = 0, d(0) = 14, indicating that the climber started with 14 liters of energy drink.

In the function c(s) = -0.4s + 12, the y-intercept (where s = 0) represents the initial volume of water the cyclist had before starting the cycling event. When s = 0, c(0) = 12, indicating that the cyclist started with 12 liters of water.

In the function w(r) = -0.3r + 18, the y-intercept (where r = 0) represents the initial volume of water the kayaker had before starting the river trip. When r = 0, w(0) = 18, indicating that the kayaker started with 18 liters of water.

In the function e(p) = -0.8p + 20, the y-intercept (where p = 0) represents the initial amount of energy bar the skier had before starting the descent. When p = 0, e(0) = 20, indicating that the skier started with 20 grams of energy bar.

In the function u(y) = -0.4y + 12, the y-intercept (where y = 0) represents the initial amount of sunscreen the swimmer had before starting the competition. When y = 0, u(0) = 12, indicating that the swimmer started with 12 ounces of sunscreen.

In the function s(h) = -0.6h + 9, the y-intercept (where h = 0) represents the initial volume of sports drink the athlete had before starting the training. When h = 0, s(0) = 9, indicating that the athlete started with 9 liters of sports drink.

In the function m(d) = -2d + 40, the y-intercept (where d = 0) represents the initial quantity of trail mix the hiker had before starting the hike. When d = 0, m(0) = 40, indicating that the hiker started with 40 ounces of trail mix.

In the function g(t) = -0.7t + 15, the y-intercept (where t = 0) represents the initial amount of energy gel the cyclist had before starting the race. When t = 0, g(0) = 15, indicating that the cyclist started with 15 grams of energy gel.