Ly is spending the day riding her bicycle in the countryside. She knows that she
ID: 3138142 • Letter: L
Question
Ly is spending the day riding her bicycle in the countryside. She knows that she will travel 8 mph on unpaved roads and will travel 12 mph on paved roads. She plans to travel total of 48 miles. a. If Ly travels x hours on unpaved roads, then___x represents the distance she travels on unpaved roads. b. If Ly travels y hours on paved roads, then ____y represents the distance she travels on paved roads. c. Combine your answers to (a) and (b) to write an equation that models this situation, using the form ax+by=c, where c is the total miles traveled.This is a graph of the equation from problem (c): On the x axis hours Riding on Unpaved Roads from 0-8 On the y axis hours Riding on Paved Roads Using the graph d. If Ly traveled the entire 48 miles on unpaved road, how long will it take her? e. Where do you see that on the graph? f. If Ly travels the entire 48 miles on paved road, how long will it take her? g. Where do you see that on the graph? h. If Ly travels on paved roads for two hours, how much time will she spend traveling on unpaved roads? Show your work or explain your reasoning. Ly is spending the day riding her bicycle in the countryside. She knows that she will travel 8 mph on unpaved roads and will travel 12 mph on paved roads. She plans to travel total of 48 miles. a. If Ly travels x hours on unpaved roads, then___x represents the distance she travels on unpaved roads. b. If Ly travels y hours on paved roads, then ____y represents the distance she travels on paved roads. c. Combine your answers to (a) and (b) to write an equation that models this situation, using the form ax+by=c, where c is the total miles traveled.
This is a graph of the equation from problem (c): On the x axis hours Riding on Unpaved Roads from 0-8 On the y axis hours Riding on Paved Roads Using the graph d. If Ly traveled the entire 48 miles on unpaved road, how long will it take her? e. Where do you see that on the graph? f. If Ly travels the entire 48 miles on paved road, how long will it take her? g. Where do you see that on the graph? h. If Ly travels on paved roads for two hours, how much time will she spend traveling on unpaved roads? Show your work or explain your reasoning. a. If Ly travels x hours on unpaved roads, then___x represents the distance she travels on unpaved roads. b. If Ly travels y hours on paved roads, then ____y represents the distance she travels on paved roads. c. Combine your answers to (a) and (b) to write an equation that models this situation, using the form ax+by=c, where c is the total miles traveled.
This is a graph of the equation from problem (c): On the x axis hours Riding on Unpaved Roads from 0-8 On the y axis hours Riding on Paved Roads Using the graph d. If Ly traveled the entire 48 miles on unpaved road, how long will it take her? e. Where do you see that on the graph? f. If Ly travels the entire 48 miles on paved road, how long will it take her? g. Where do you see that on the graph? h. If Ly travels on paved roads for two hours, how much time will she spend traveling on unpaved roads? Show your work or explain your reasoning.
Explanation / Answer
Distance = speed x time.
a. Distance travelle don unpaved roads = 8x
b. Distance travelle don paved roads = 12y
c. 8x + 12y = 48 (Total distance travelled)
d. 12y = 0 ==> 8x = 48 ==> x = 6 hours
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