Question

Krisha’s school is 40 miles away. She drove at a rate of 40 mph (miles per hour) for the first half of the distance, then 60 mph for the remainder of the distance. What was her average speed for the entire trip?

Answer 1

`v_(avg)=48"mph"`

Explanation:

Lets split this in to two cases, the first and second half trip

1. She drives the distance `s_1=20`,
   with the velocity `v_1=40`

2. She drives the distance `s_2=20`,
   with the velocity `v_2=60`

The time for each case must be given by `t=s/v`

The time it takes to drive the first half:
`t_1=s_1/v_1=20/40=1/2`

The time it takes to drive the second half:
`t_2=s_2/v_2=20/60=1/3`

The total distance and time must be respectively

`s_"total"=40`

`t_"total"=t_1+t_2=1/2+1/3=5/6`

The average velocity

`v_(avg)=s_"total"/t_"total"=40/(5/6)=(6*40)/5=48`