Question 212330: Joan ran from her home to the lake at 8mi/h.She ran back home at 6mi/h. Her total running time was 32 minutes. How much time did it take joan to run from her home to the lake. ok I get the problem 8(t)= 6( )= 32 but what do i put in the second set and ho do i go on from there?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! HOPE THIS HELPS---ON THESE PROBLEMS YOU EITHER HAVE TO DEAL IN MINUTES OR HOURS---YOU CAN'T MIX. I WILL DEAL IN HOURS:
Distance(d) equals Rate(r) times Time(t) or d=rt;r=d/t and t=d/r
Let t1=time to the lake
Let t2 equal time from the lake
Now we are told that t1+t2=32/60 =8/15 hr---------------eq1
distance to the lake =8t1
distance from the lake =6t2
We know that distance to lake=distance from lake, so:
8t1=6t2------------------------------------------eq2
From eq2, t2=(4/3)t1. Substitute this for t2 in eq1:
t1+(4/3)t1=8/15
(7/3)t1=8/15 multiply each side by 15
35t1=8
t1=8/35 hr--------------------------Time for Joan to run from home to the lake
ANOTHER WAY::
Let d=the distance to/from home to lake
Time to run from home to the lake=d/8
Time to run back from the lake to home=d/6
And we are told that the above two times add up to 32/60 or 8/15 hr, so:
d/8 +d/6 = 8/15 multply each term by 120
15d+ 20d=64
35d=64
d=64/35 mi
So time for Joan to run from her home to the lake=(64/35)/8=8/35 hr
And time for Joan to run back home=(64/35)/6=64/210 hr
CK
Total time then is: 8/35 + 64/210=48/210 + 64/210=112/210=8/15 hr
Hope this helps---ptaylor
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