This week in Math 10 I learned how to solve word problems using time, speed, and distance applications.
Imagine this is the word problem:
A student drove 1245km from Edmonton to Vancouver in 16 hours. This included a one hour stop in Golden Ears and a 30 minute stop in Kamloops. She averaged 100km/h on the divided highways and 75km/h on the non-divided mountainous roads. How much time did she spend on the divided highways?
To solve this, there are two key factors we must know; how to create a grid, and common sense.
Because distance, speed, and time are used in this word problem, we are using it to find how much time was spent on the divided highways.
We are first going to fill in everything we know point-blank about the world problem. It says they averaged 100km/h on the highway and 75km/h on the mountains. We also know the total distance driven, which is 1245km. It also says in the word problem that it took 16 hours to drive from Edmonton to Vancouver, so why are there 15 hours on the grid and not 16? This is where common sense comes in. There were 16 hours total throughout the whole trip, however, because of the one hour and half hour stops, she spent 15 hours purely driving.
Now we fill in what we don’t know, which is represented by x and y. We don’t know the time that was spent driving on the highway or the mountains.
Now we add to create an equation. Because x and y represent the time on the highway and mountain, we will be replacing the hours in the speed with X. The result is 100x and 75y.
Now we simply add up the columns, giving us the equations:
x + y = 15
100x + 75y = 1245
At this point, answer the equations using substitution, elimination, or graphing (don’t).