Question

A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at a rate of 40 miles per hour, what is the average speed for the entire trip, in miles per hour? (Pls explain throughly with your answer)

Answer 1

Answer:

80/3

Step-by-step explanation:

same distance is covered at different speed , avg speed= 2ab/a+b

= 2*20*40/60

= 80/3

Answer 2

Answer:

$\frac{80}{3}\text{ mph}$

Step-by-step explanation:

We can use the formula $d=rt$ (distance  = rate * time) to solve this problem.

If the motorist is travelling 90 miles to and back on a trip, he has travelled $90+90=180$ miles total. This represents $d$ 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:

$90=20t,\\t=\frac{90}{20}=\frac{9}{2}=4.5$ 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:

$90=40t,\\t=\frac{90}{40}=\frac{9}{4}=2.25$ hours

Therefore, the total time is $4.5+2.25=6.75$ hours.

Now can calculate the average speed of the entire trip:

$180=6.75r,\\r=\frac{180}{6.75}=\frac{180}{\frac{27}{4}}=180\cdot \frac{4}{27}=\boxed{\frac{80}{3}\text{ mph}}$