## 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?

January 28th, 2011 at 1:50 pm

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

add them

30t + 30t = 60t

Average over x axis

60t/2.5t = 24mph

January 28th, 2011 at 1:51 pm

24 MPH.

time = dist / speed = x/30 + x/20 = x/12

speed = dist / time = 2x/(x/12) = 24

January 29th, 2011 at 1:57 pm

24 mph.

January 29th, 2011 at 11:49 pm

25 mile per hour

January 29th, 2011 at 11:52 pm

25 mile per hour

Its really quite simple

add the two speeds and divide by 2

This will give you the average speed

January 30th, 2011 at 6:35 am

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.

January 31st, 2011 at 7:11 am

Thank you Mike for the swift and correct answer

February 1st, 2011 at 6:22 am

24 mph

February 1st, 2011 at 4:00 pm

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