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

80/3

Explanation:

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

= 2*20*40/60

= 80/3

Answer 2

`(80)/(3)\text{ mph}`

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=(90)/(20)=(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=(90)/(40)=(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=(180)/(6.75)=(180)/((27)/(4))=180\cdot (4)/(27)=\boxed{(80)/(3)\text{ mph}}`