Answer:
[tex]\frac{80}{3}\text{ mph}[/tex]
Step-by-step explanation:
We can use the formula [tex]d=rt[/tex] (distance = rate * time) to solve this problem.
If the motorist is travelling 90 miles to and back on a trip, he has travelled [tex]90+90=180[/tex] miles total. This represents [tex]d[/tex] in our formula.
Now we need to find the total time.
On the first trip, it's given that the motorist travels at a rate of 20 mph. Therefore, the time this trip took to travel 90 miles is:
[tex]90=20t,\\t=\frac{90}{20}=\frac{9}{2}=4.5[/tex] hours
On the second trip back, he travels the same distance (90 miles) at a rate of 40 mph. Therefore, the time the trip took is:
[tex]90=40t,\\t=\frac{90}{40}=\frac{9}{4}=2.25[/tex] hours
Therefore, the total time is [tex]4.5+2.25=6.75[/tex] hours.
Now can calculate the average speed of the entire trip:
[tex]180=6.75r,\\r=\frac{180}{6.75}=\frac{180}{\frac{27}{4}}=180\cdot \frac{4}{27}=\boxed{\frac{80}{3}\text{ mph}}[/tex]
