Question

I need help solving the following problem:
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.
a. Define a variable for the time Juan takes to travel to work.
b. Write an expression for the time Juan takes to return home.
c. Write and solve an equation to find the time Juan spends driving to work. Make sure to show your work.

Answer 1

a. remember that average speed is the total distance travelled divided by the total time. Going to work we have:\[22=d/t\]Rearranging we get\[t _{1}=d/22\]We don't know d or t, yet.

b. To get home we have
\[32=d/t _{2} \rightarrow t _{2}=d/32\]

c. The total time is given in the problem as 2.25 hours. This is the sum of the times given in part a,b.
\[t _{1}+t _{2}=\frac{d}{22}+\frac{d}{32}=2.25\]Solving for d we get:\[\frac{54d}{704}=2.25\]So,\[d \approx29.3\]. The question asks for the time Juan spent driving to work. Going back to part a, we input d=29.3 into the equation we had there:\[t _{1}=d/22=29.3/22\approx1.33\]So it took him about 1.33 hours to get to work.