David travels one-third of the distance from LA to SF at a s

(Average speed) = (total distance)/(total time).

Say the distance from LA to SF is d miles, then (Average speed) = (total distance)/(total time) = \(\frac{d}{\frac{(\frac{d}{3})}{40}+\frac{(\frac{2d}{3})}{80}}=\frac{d}{\frac{d}{120}+\frac{d}{120}}=60\) miles per hour.

Answer: D.

P.S. Please name the topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html

Also, please tag the topics properly: this is a distance/rate problem, not arithmetic.

Thank you.

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Lets say he travels total 3 Miles........ (1)

So, speed for 1 mile = 40
Speed for next 2 miles = 80

Total time taken \(=\frac{1}{40} + \frac{2}{80} = \frac{2}{40}\)........ (2)

\(Average = \frac{Total distance}{Total time}\)

\(= 3 * \frac{40}{2}\)

= 60

Answer = D

Another way to solve the question is by assuming the distance which will avoid the unwanted calculation of fractions

Let's assume the distance which is divisible by 3 as 1/3 Distance is Travelled @40 mph
also Let's assume a distance that is divisible by 40 and 80 as well as TIME = DISTANCE/SPEED and Speeds are 40 and 80 mph

Let, Distance = 240 Miles

1/3 Distance = (1/3)*240 = 80 miles is Travelled @40 mph

i.e. TIME TAKEN = Distance / Speed = 80/40 = 2 hours

2/3 Distance = (2/3)*240 = 160 miles is Travelled @80 mph

i.e. TIME TAKEN = Distance / Speed = 160/80 = 2 hours

TOTAL DISTANCE = 240
TOTAL TIME = 2+2 = 4 Hours

AVERAGE SPEED = TOTAL DISTANCE / TOTAL TIME = 240/4 = 60 mph

Answer: option
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We can use the average speed equation:

average speed = total distance/total time

We can also let the total distance be 600 miles. Therefore, we have:

average speed = 600/(200/40 + 400/80)

average speed = 600/(5 + 5)

average speed = 600/10

average speed = 60 mph

(Note: We can choose any number for the total distance between the two cities. In this case, 600 is a convenient number, making the resulting arithmetic easy to perform without a calculator.)

Answer: D
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