Question 187209

WOULD IT HELP IF I SET IT UP AND YOU ANSWER IT?  OK.  I'LL SET IT UP.

Distanced(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let r=her speed during the first part of the trip
Then r-10= her speed during the second part of the trip
time for first part of trip=120/r
time for second part of trip=100/(r-10)
And we are told that the sum of the above two times equals 4 hrs, so:

120/r +100/(r-10)=4  multiply each term by r(r-10)
120(r-10)+100r=4r(r-10)  get rid of parens
120r-1200+100r=4r^2-40r  subtract 4r^2 from and add 40r to both sides
120r-1200+100r-4r^2+40r=0  collect like terms
-4r^2+260r-1200=0  divide each term by -4
r^2-65r+300=0  quadratic in standard form and it can be factored:
(r-60)(r-5)=0
By inspection, we can see that 5 is no good because when we subtract 10 from it, we get a negative speed and that's not good.

I think you can take it from here

Hope this helps---ptaylor