Problem Solving

Finding an answer of the following question is easy. I need help to understand why are we not getting the right answer if we do it by weighted average. Pls explain how u solved preferably through weighted average. OA to follow.

QUESTION:

Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip7

A) 35

B) 40

C) 45

D) 50

E) 55

avg speed formula when distance is same

[speed1 * speed2 * 2] / (speed1 + speed2)

30*60*2 / 30+60 = 40

Hope this helps.

understand. My issue is to understand from weighted average perspective? - what am i doing wrong in weighted average ?

1/2(30) + 1/2(60) = 45

a slightly different approach

D R T
case(1) 30 30 1
case(2) 30 60 1/2
------------------------------------------------------
total 60 40 3/2

avg rate = 120/3 = 40

understand. My issue is to understand from weighted average perspective? - what am i doing wrong in weighted average ?

1/2(30) + 1/2(60) = 45

it seems you are following a different formula

should be ----> total distance/total time; in this case
total distance=30+30=60
total time=1+1/2=3/2

so 60/3/2=60*2/3=120/3=40[/quote]

Can anyone please discuss this from weighted average perspective?

I totally understand total distance / total time formula for total averages. What's wrong applying weighted average here though?

When you use the weighted average method you must weight by time instead of by distance. Therefore, the correct weighted average formula is as follows:

30mph*(1.0hrs/1.5hrs) + 60mph*(0.5hrs/1.5hrs) = X

Solving for x,

30mph*(2/3hrs) + 60mph*(1/3hrs) =

20mph + 20mph = 40mph

Therefore, the correct answer is (B).

jba05d wrote:When you use the weighted average method you must weight by time instead of by distance. Therefore, the correct weighted average formula is as follows:

30mph*(1.0hrs/1.5hrs) + 60mph*(0.5hrs/1.5hrs) = X

Solving for x,

30mph*(2/3hrs) + 60mph*(1/3hrs) =

20mph + 20mph = 40mph

Therefore, the correct answer is (B).

Great, thanks ! thats the concept i want to clarify.