SOLUTION: I have absolutely no idea how to solve this problem. I have a few other distance problems on my homework assignment and I didn't have too much trouble with them, I just have no ide

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Question 963224: I have absolutely no idea how to solve this problem. I have a few other distance problems on my homework assignment and I didn't have too much trouble with them, I just have no idea how to do this one:
Nina went to the college traveling 6 mph and returned home traveling 12 mph. If the total trip took 9 hours, how long did Nina travel at each speed?
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates, Travel, VT=D for rate time distance relationship.

____________________speed____________time__________distance
GOING________________r_______________(___)__________d
BACK_________________R______________(____)__________d
Total________________________________t

The data table has variables assigned as r=6, R=12, t=9, and d is unknown.

The rule VT=D gives T=D/V;
The general rule is using V as rate instead of R, because I already assigned R a specific value according to your problem's description.

____________________speed____________time__________distance
GOING________________r_______________d/r__________d
BACK_________________R______________d/R__________d
Total________________________________t

You have an obvious time sum equation:
highlight_green%28d%2Fr%2Bd%2FR=t%29.
Solve this equation for d. Lowest common denominator is r%2AR.

%28d%2Fr%2Bd%2FR%29%2Ar%2AR=t%2Ar%2AR
dR%2Bdr=trR
d%28R%2Br%29=trR
highlight%28d=%28trR%29%2F%28r%2BR%29%29

Substitute the given values for t, r, and R and evaluate d.

You can go back now and evaluate the two time terms, d%2FR and d%2Fr.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Nina went to the college traveling 6 mph and returned home traveling 12 mph. If the total trip took 9 hours, how long did Nina travel at each speed?
==================
Avg speed of a round trip = 2*r1*r2/(r1+r1) - r1 and r2 are the 2 speeds
Avg = 2*6*12/(6+12) = 8 mi/hr
RT distance = 8*9 = 72 miles --> 36 miles each way.
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t = d/r
t = 36/6 = 6 hours going
t = 3 hours returning