SOLUTION: A reconnaissance plane flies 514 km away from its base at 596 m/s, then flies back to its base at 894 m/s. What is its average speed? Answer in units of m/s.

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Question 1123816: A reconnaissance plane flies 514 km away from
its base at 596 m/s, then flies back to its base
at 894 m/s.
What is its average speed?
Answer in units of m/s.
Found 4 solutions by josgarithmetic, ikleyn, MathTherapy, Alan3354:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
Notice distance is kilometers but the speeds given are in METERS per SECOND. Decide which speed unit you need for your result and convert whatever this requires.

1 kilometer is 1000 meters.
60 seconds is 1 minute.
60 minutes is 1 hour.

--
596%28m%2Fs%29%281%2F1000%29%28km%2Fm%29%2A3600%28s%2Fhour%29
596%2836%2F10%29
596%2818%2F5%29
2145.6%28km%2Fhour%29speedgoing
-
894%2818%2F5%29
3218.4%28km%2Fhour%29speedreturning
-

Total Distance, 2%2A514=1028 kilometers

Total Time, 514%2F2145.6%2B514%2F3218.4 hours
or 0.3993 hours.

Average Speed:
1028%2F0.399267
2570 kilometers per hour, to three significant figures

Answer by ikleyn(52755) About Me  (Show Source):
You can put this solution on YOUR website!
.
Total two-ways distance is 2*514 kilometers = 1028 kilometers = 1028000 meters.


Total time = 514000%2F596 + 514000%2F895 seconds.


Average speed = total_two_ways_distance%2Ftotal_time = 1028000%2F%28514000%2F596%2B514000%2F894%29 = 2%2F%281%2F596%2B1%2F894%29 = %282%2A596%2A894%29%2F%28894%2B596%29 = 715.2 m/s

Solved.

-------------------

Two lessons to learn from this solution : 

    1.  From the solution, learn the method of calculating average speed.


    2.  In this problem (as in other two-ways problems) the average speed does not depend on a one-way distance. 


        The average speed = %282%2AV%5B1%5D%2AV%5B2%5D%29%2F%28V%5B1%5D%2BV%5B2%5D%29.


For other similar problems, see the lessons
    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed
in this site.


Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
A reconnaissance plane flies 514 km away from
its base at 596 m/s, then flies back to its base
at 894 m/s.
What is its average speed?
Answer in units of m/s.
Total distance: 2(514,000), or 1,028,000 m

Total time: 

Average speed: 

IGNORE ALL NON-SIMILAR answers!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Planes (and boats) don't use meters/sec for speed.
They use knots.