SOLUTION: Juan traavels 22mi/hr to work and 32mi/hr back home. It takes him a total of 2 hrs and 15 minutes for the total drive. I need to find an equation on how much time it takes Juan to

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Question 232346: Juan traavels 22mi/hr to work and 32mi/hr back home. It takes him a total of 2 hrs and 15 minutes for the total drive. I need to find an equation on how much time it takes Juan to go to work and come back home. I also need an equation for both. Thank you
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
OK
I'm not sure that I fully understand what you are looking for in terms of equations but I will give it a shot:
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let t1=time to go to work
And let t2=time to come back home
Now we are told that:
t1+t2=2.25 hrs (we'll deal in hours)------------------------eq1
We also know the following:
Distance to work=22t1
Distance back to home=32t2
We know that the above two distances are equal, so:
22t1=32t2 or
11t1=16t2---------------------eq2

Now from eq2, we see that t2=(11/16)t1 and t1=(16/11)t2; First, substitute t2=(11/16)t1 into eq1 and we get:
t1+(11/16)t1=2.25hr (Note: 11/16 = 0.6875)
t1+0.6875t1=2.25
1.6875t1=2.25 Equation for the time it takes Juan to go to work
Next, substitute t1=(16/11)t2 into eq1 and we get:
(16/11)t2+t2=2.25 (Note:16/11 = 1.455)
t2+1.455t2=2.25
2.455t2=2.25----equation for the time it takes Juan to get home
CK
1.6875t1=2.25
t1=1.33333 hours
2.455t2=2.25
t2=0.9165 hr
1.33333hrs+0.9165hrs=about 2.25hrs

Hope this helps---ptaylor