Use the distance formula to create the system of equations. Then, use the information from the exercise to substitute a value for one of the variables.
A
1.25 hours
B
0.5 miles
Practice makes perfect
We want to know how long it will take for us to catch up to our friend in the canoe race. Let's take a look at the given photo.
d=rt
In this formula, r is the rate of speed, d is the distance traveled, and t is time spent traveling. With this in mind, let's focus on the system of equations. From the exercise, we know that our friend is padding 3 miles per hour and is 0.5 miles ahead of us. We are padding at 3.4 miles per hour. We are ready to write the system of equations!
d= 3t+ 0.5 & (I) d= 3.4t & (II)
Now we will graph each equation and look for a point of intersection, which will be the solution to the system of equations.
The graphs seem to intersect at the point (1.25,4.25). Let's check if this point is a solution to the system of equations we created. We can check by substituting 1.25 for t and 4.25 for d in each equation and checking whether they result in a true statement.
We found that the solution to the system is (1.25,4.25). This means that we will catch up with our friend after 1.25 hours.
We want to find out how far ahead we will be of our friend when we cross the finish line of the canoe race. Let's use our system of equations again.
d= 3t+ 0.5 & (I) d= 3.4t & (II)
We know that we are 8.5 miles from the finish line, so let's substitute 8.5 for d in the formula for speed and find how much time we need to finish the race. We can then use this information to calculate how far behind us our friend is. Let's do it!
We found that we will cross the finish line after 2.5 hours. Let's substitute 2.5 for t in the second equation to calculate where our friend will be at that time.
