# Average speed of a plane

Suppose a plane flies 3470 miles from New York to London at an average speed of 1810 mi/h. Then the plane leaves London and flies to Los Angeles 5460 miles away with an average speed of 1437 mi/h. Find the average speed.

I know that v(avg) = (delta)X/(delta) T.

But my question is how do you find the average speed? is it distance 1 + distance 2 divided by speed 1 + speed 2?

or

is it Distance 1/speed one + distance 2 divided by speed 2, and then add the two answers together ?

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The average speed is going to have to be weighted by the distance traveled at each leg. With a little thought, this makes sense. Suppose you are going 10mph for 100 miles, and 5 mph for 4 miles, your average speed will not simply be 10+5/ 2 = 15/2 mph. You were going a stead 10mph for nearly 100 miles, thats more than 25 times longer than when you were going 5mph. So your average speed should be very close to 10mph. See if you can apply this reasoning to find out how to "weight" the given average speeds to come up with the total average speed of the trip.

Are you trying to find the average distance of each individual trip or the whole flight? I believe reguardless of the speeds/trips, to find the average speed it is distance divided by time. If it took you 4 hours to go from Point A to Point B with distance = 100 miles, your AVG speed is 25mph. If it took you 3 hours to go from B to Point C with distance = 150 miles, your AVG speed is 50mph. Therefore, to go from A to C, you traveled 250 miles in 7 hours, your AVG speed was 250/7=35.7 mph.

The weighting idea is correct, but I see things slightly more simply than that. As everyone has been saying, average speed is distance over time. So, for the WHOLE TRIP what is the distance travelled? Then divide that by the time taken for the WHOLE TRIP.

Note: If you are doing average velocity as opposed to average speed, you need to be careful about the vector nature of velocity, or more precisely, displacement. For instance, if you complete a round trip of 5000 miles in 2 days, your average speed is 2500 mi/day. The average velocity would deal with the overall displacement, which has a zero magnitude, so the average velocity of the round trip would have a magnitude of 0 mi/day.

-Dan