Juan drives to work. Because of traffic conditions, he averages 22 miles per hour. He returns home averaging 32 miles per hour. The total travel time is 2 1/4 hours.
Define a variable for the time Juan takes to travel to work.
Write an expression for the time Juan takes to return home.
Writeand Solve equation to find the time Juan spends driving to work.
Use the relationship that
distance = rate x time and follow the instructions in the problem.
To define a variable for the time Juan takes to travel to work, let's use the variable "t". So, "t" represents the time Juan takes to travel to work.
To write an expression for the time Juan takes to return home, we can use the equation:
Total travel time = Time to travel to work + Time to return home
Since we know the total travel time is 2 1/4 (or 2.25) hours, and we already defined "t" as the time Juan takes to travel to work, we can rewrite the equation as:
2.25 = t + Time to return home
Now, let's solve the equation to find the time Juan spends driving to work:
Given that Juan averages 22 miles per hour while going to work, we can use the equation:
Distance = Speed × Time
Since the distance Juan travels to work is the same as the distance he travels back home (assuming the route is the same), we can write:
Distance to work = Distance back home
Speed × Time to work = Speed × Time back home
22t = 32 × Time back home (since Juan averages 32 miles per hour while returning home)
Now, let's substitute the expression for Time back home from the first equation into the second equation:
22t = 32 × (2.25 - t)
Now we can solve for "t".