Question 579987
A train went 400 miles from city A to city B at a speed of 80 mph . At what speed should it travel on the way back if wants to have an average speed of 96 mph for the entire round-trip journey ?

I got answer 112.

x = 2nd speed.

(80+x)/2=96

x = 112

but some say it should be 120. How?
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Averaging two speeds like that, (s1 + s2)/2 doesn't work, because more time is spent moving at the lower speed.
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A train went 400 miles from city A to city B at a speed of 80 mph . At what speed should it travel on the way back if wants to have an average speed of 96 mph for the entire round-trip journey ?
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It went 400 miles at 80 mi/hr = 5 hours
800 miles @ 96 mi/hr = 800/96 = 25/3 hours for the round trip.
25/3 - 5 = 10/3 hours to return
400 mi/(10/3)hr = 120 mi/hr
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PS  The avg speed of a round-trip (or 2 equal distances) is
2*v1*v2/(v1 + v2)  where v1 and v2 are the 2 speeds.
For this one,
avg = 2*80*120/(80 + 120) = 96 mi/hr