Question

Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole trip?

Answer 1

47.37 miles per hour,

Step-by-step explanation:

The average speed is given by the formula

Average speed =(total distance / total time)

Let the distance Joe traveled at a speed of 45 miles per hour be 'D', because he then drove the same distance with a speed of 50 miles per hour then, the total distance is '2D'.

The total time will be the time he drove at a speed of 45 miles per hour (
`t_(1)`) plus the time he drove at a speed of 50 miles per hour (
`t_(2)`).

Then the average speed is :

`v_(average) = (2D)/(t_(1)+t_(2))`.

Because we know that uniform rectilinear motion is discribed by the ecuation

`d=\v*t` (where d is distance, v is a constant speed and, t is the time)

we can express both times in terms of speeds and the distance, thus

`t_(1) =(D)/(v_(1))` and,

`t_(2) =(D)/(v_(2))`.

So now the average speed
`v_(average) = (2D)/(t_(1)+t_(2))` can be written as follows:

`v_(average) = (2D)/(((D)/(v_(1))+(D)/(v_(2)) ))`

`v_(average) = (2D)/(D((1)/(v_(1))+(1)/(v_(2)) ))`

`v_(average) = (2)/(((1)/(v_(1))+(1)/(v_(2)) ))`

`v_(average) = (2)/(((1)/(45)+(1)/(50) ))`

`v_(average) = 47.37` miles per hour.

Answer 2

`v_(avg) = 49.5 mph`

Step-by-step explanation:

Let the distance moved by Joe is "d"

so the time taken by him to drove it by speed 45 mph is given as

`t_1 = (d)/(v_1)`

`t_1 = (d)/(45)`

now the same distance is traveled by him with speed 55 mph

so the time taken by him

`t_2 = (d)/(55)`

so total time taken by him for complete distance 2d

`t = t_1 + t_2`

`t = (d)/(45) + (d)/(55)`

`t = 0.0404 d`

now the average speed is given as

`v_(avg) = (2d)/(t)`

`v_(avg) = (2d)/(0.0404d)`

`v_(avg) = 49.5 mph`