Jaun drives to work. he averages 22mph,
he returnes home averaging 32mph. total travel time is 2.25 hours.
a. define a variable for the time Jaun takes to travel to work. write an exprension for the time it takes to return home.
b. write and solve an equation to find the time Jaun spends driving to work.
Let d be the distance, t1 time to work, t2 the time to come back.
d=22*t1
d=32*t2 or
22t1=32t2 or
t1=32t2/22= 16/11 t2
t1+t2=2.25hrs
16/11 t2+t2= 2.25 solve for t1, then go back and solve for t1.
a. Let's define the variable "x" as the time Juan takes to travel to work.
Since the distance Juan travels to work is constant, we can use the formula: distance = speed × time.
So, for the time it takes Juan to return home, we can use the formula: distance/rate = time.
Let "y" represent the time it takes to return home.
b. To find the time Juan spends driving to work, we can set up an equation using the given information.
We know that the total travel time is 2.25 hours. So, the time it takes to travel to work (x) plus the time it takes to return home (y) is equal to 2.25:
x + y = 2.25
Now, let's solve this equation to find the value of "x".
We know that Juan's average speed on the way to work is 22 mph. So, the distance he travels can be calculated using the formula: distance = speed × time:
distance = 22x
Similarly, Juan's average speed on the return journey is 32 mph. Therefore, using the same formula, the distance he travels on the return journey is:
distance = 32y
Since the distances traveled to work and back are the same, we can set up another equation:
22x = 32y
Now we have a system of two equations:
x + y = 2.25 (Equation 1)
22x = 32y (Equation 2)
To solve for "x", we can use substitution or elimination:
Let's use substitution. Rearrange Equation 1 to solve for "y":
y = 2.25 - x
Substitute this expression for "y" into Equation 2:
22x = 32(2.25 - x)
Now, we can solve this equation to find the value of "x":
22x = 72 - 32x
54x = 72
x = 1.33
Therefore, Juan spends approximately 1.33 hours, or 1 hour and 20 minutes, driving to work.