Lance is 30 km from home. He rides his bike with a constant speed of 12 km/h. Make a graphical illustration of the number of hours and the number of kilometers he is from home. How long before he is home?
show your complete solution
Share
Lance is 30 km from home. He rides his bike with a constant speed of 12 km/h. Make a graphical illustration of the number of hours and the number of kilometers he is from home. How long before he is home?
show your complete solution
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
To solve this problem, you should first convert the information from the exercise to a function. The formula for a straight line is almost suitable, since Lance is riding his bike with constant speed. Here, you see how words and expressions are converted to mathematical symbols.
[tex]\:[/tex]
When solving this problem you should think like this: Since the text informs us that Lance is 30 km away from home and that he is riding his at 12 km/h, his journey begins at 30 km and the closer he gets to home, the smaller the distance. Thus, you convert the information like this:
[tex]\:[/tex]
Now you insert this in the formula for a straight line f(x) = mx + b and get:
[tex]\sf{\:\:\:\:\:f(x)\:=\:-12x\:+\:30}[/tex]
[tex]\:[/tex]
30 is the constant term since the starting point for Lance is set. -12 is the slope since the distance to home is reduced by 12 km for every hour Lance rides his bike towards home.
[tex]\:[/tex]
Note! The minus sign for Lance's speed does not mean that he backs up all the way home. The minus sign is used to count down from 30 km to 0 km. The distance should decrease and therefore you need a minus sign to accomplish this.
[tex]\:[/tex]
Based on the expression above you get the following function table:
[tex]\footnotesize\begin{gathered}\begin{gathered}\begin{gathered}\begin{array}{|c|c|c|} \hline \small \sf x & \sf y\:=\:f(x)\:=\:-12x\:+\:30 & \sf (x,\:y) \\ \hline \sf 0 & \sf f(0)\:=\:-12\:·\:0\:+\:30\:=\:30 & \sf (0,\:30) \\\hline \sf 0.5 &\sf f(0.5)\:=\:-12\:·\:0.5\:+\:30\:=\:24 & \sf (0.5,\:24) \\\hline \sf 1 & \sf f(1)\:=\:-12\:·\:1\:+\:30\:=\:18 & \sf (1,\:18) \\ \hline \sf 1.5 & \sf f(1.5)\:=\:-12\:·\:1.5\:+\:30\:=\:12 & \sf (1.5,\:12) \\ \hline \sf 2 & \sf f(2)\:=\:-12\:·\:2\:+\:30\:=\:6 & \sf (2,\:6) \\ \hline \sf 2.5 & \sf f(2.5)\:=\:-12\:·\:2.5\:+\:30\:=\:0 & \sf (2.5,\:0) \\ \hline \sf 3 & \sf f(3)\:=\:-12\:·\:3\:+\:30\:=\:-6 & \sf (3,\:-6) \\\hline \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex]\:[/tex]
From the function table, you see that Lance gets home after x = 2.5 hours. Since the problem ask you to solve this graphically, you now have to make a coordinate system in which you mark the points you have calculated and written in the column with (x, y), and then draw the line between them. The graph should look like this:
[tex]\:\:\:\:\:\:\:\:\boxed{\sf{See\:the\: picture}}[/tex]
[tex]\:[/tex]
Lance arrived at home when the y - coordinate is 0. This is when the graph intersects the x-axis. The circle marks this point and you can see that Lance arrives at home after x = 2.5 hours. Thus, the answer is:
It takes 2.5 hours before Lance arrives at home.
[tex]\:[/tex]
[tex]\:[/tex]
#CarryOnLearning