SOLUTION: 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-
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> SOLUTION: 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-
Log On
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?
Thanks.
You can put this solution on YOUR website! 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?
---------------------------
Averaging two speeds like that, (s1 + s2)/2 doesn't work, because more time is spent moving at the lower speed.
------------
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 ?
------------
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
----------------
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
You can put this solution on YOUR website!
Entire round trip journey = 800 miles
solve for time:
t = 800 / 96 mph = 8 1/3 hours needs to be total time
already used:
t = 400 / 80 = 5 hours
3 1/3 hours left to go 400 miles back, solve for speed:
v = 400 / (3 1/3) = 120 mph
its not a simple average, since the train spends different times at each speed
CHECK:
800 miles, total time 8 1/3 hours
average mph = miles/hours = 800 / (8 1/3) = 96
