How does the distance traveled relate to the rate?
B
b
How does distance traveled relate to the rate?
C
c
How are the two measures for hours from A and B related?
A
a
d/60
B
b
d/40
C
c
Equation: d60+1= d40
Distance: 120 miles Rate: 48 miles per hour
Practice makes perfect
a
We have been asked to create an expression to represent the time it took the family to travel to their relatives' house, given that d is the distance in miles. The only other information we have is they traveled at an average rate of 60 mi/h. Let's recall the relationship between distance d, time t, and rate r.
d= r * tWe need to solve for t to find the correct equation for us to use.
We have been given that the distance for the trip is d and the rate traveled is 60 mi/h. Let's substitute these values into the above formula.
d/60 mi/h = d/60
b
We can create a formula for the return trip in the same way. The distance for the return trip is d and the rate traveled is 40 mi/h. Substituting this into the above formula, we get the expression:
d/40 mi/h= d/40
c
Both expressions that we have created represent the number of hours it took to travel that particular part of the trip. However, it took 1 extra hour for the family to return home. This means that if we add an hour to the first part of the trip, the two measures of time will be equal. Let's write the equation.
d/60+ 1=d/40
Now that we have an equation, we can solve it in order to find the distance that the family traveled for each part of the trip. We can start by multiplying both sides of the equation by a common multiple in order to eliminate the fractions.
The distance that the family traveled to the relatives' house was 120 miles. To find the average speed, we need to know how long each portion of the trip took. We can use the expressions that we created in the previous parts. Let's substitute the value of d, 120, into each expression and simplify.
Part of the trip
Expression
Simplify
On the way to relative's
d/60=120/60
2
On the way home
d/40=120/40
3
As we can see, the family spent 5 hours in total on the road between the two parts of the 2* 120= 240 mile long trip. We can find the average rate by dividing the total miles by the total time.
Average Rate=240/5=48
Therefore, the family traveled at an average rate of 48 miles per hour.
