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## Nice Easy One for the Weekend

Posted by Karl Sharman on January 28, 2011 – 1:10 pm

A car travels at a speed of 30 mph from A to B, a distance “x” , and then return from B to A over the same distance “x” at a speed of 20 mph. What is the average speed for the total trip?

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This post is under “Tom” and has 9 respond so far.

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1. 1. mike Said：

In a a graph where
X = time in units (t)
Y = speed in units (mph)

y = 30 when x = 0 to t
y = 20 when x = t to 1.5t

Take the area under the graph:
30mph * t = 30t
20mph * 1.5t = 30t

30t + 30t = 60t

Average over x axis
60t/2.5t = 24mph

2. 2. DP Said：

24 MPH.
time = dist / speed = x/30 + x/20 = x/12
speed = dist / time = 2x/(x/12) = 24

3. 3. Rohan Said：

24 mph.

4. 4. brett Said：

25 mile per hour

5. 5. brett Said：

25 mile per hour
Its really quite simple
add the two speeds and divide by 2
This will give you the average speed

6. 6. Chris Said：

Hi brett. You cannot simply take the average of the two speeds.

For concreteness, let A and B be 60 miles apart. The outward journey, at 30 mph, woulf take 2 hours. The return journey, at 20 mph, would take 3 hours.

The average speed for the round trip is the total distamce travelled divided by the total time taken = 120/5 = 24 mph.

7. 7. Karl Sharman Said：

Thank you Mike for the swift and correct answer

8. 8. Serik Said：

24 mph

9. 9. mike Said：

hah, woot. Totally did it graphically though : P. I got bugged trying to do it a different way.

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