dkj1984 wrote:

Example 2.

An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices.

Hi ,

Can someone please let me know what would be the average sped in this case .

Will it be total distance / total time = 150 / 3 or will it be 2ab/a+b = 2(30*60) / 90

Please advise.

Thanks!

Regards,

Divya

I will clear your doubt but first let me give you some unsolicited 'gyan'.

When dealing with formulas, remember two things:

1. Do not learn up formulas without knowing the assumptions made to derive them.

2. Make sure you understand how they are derived and the starting point.

Average speed is always Total Distance/Total Time.

1. The formula 2ab/(a+b) assumes that the distance traveled at speed a is the same as the distance traveled at speed b. Say distance traveled in each case is 1 km.

2. Derivation:

Average Speed = Total Distance/Total Time = (1+1)/(1/a + 1/b) = 2ab/(a+b)

So in case you have three speeds a, b and c, you know how to get the average speed in that case too.

Coming to this question, the formula is not used here because it doesn't say that the distance traveled at the two speeds is the same.

Average Speed = Total distance/Total Time = 150/3 = 50 km/hr

Now there are two ways to handle it:

1. Weighted averages

2. Using algebra

Weighted Averages Method:

This now becomes a weighted average problem since you have two speeds and their average is known. The weights will be the time for which the speeds were maintained.

w1/w2 = (60 - 50)/(50 - 30) = 1:2

So plane travel lasted 2 hrs and car travel lasted 1 hr.

Distance traveled by plane = 2*60 = 120 km

Algebra Method:

Let time for which he traveled by plane is t hrs.

50 = (t*60 + (3-t)*30)/3

150 = 60t - 30t + 90

t = 2 hrs

So plane travel lasted 2 hrs.

Distance traveled by plane = 2*60 = 120 km

For more on weighted averages method (which helps you solve orally), check:

http://www.veritasprep.com/blog/2011/03 ... -averages/Thanks for the solution. However, please explain why the "The weights will be the time for which the speeds were maintained" in the weighted average method. How is the ratio of average speed giving us the ration of time ?