Question 106224
d=st d=distance, s=speed, t=time
d=200 miles, s=Steve's speed in mph, t= his time in hrs
The distance of both trips is the same. So,:
st=200
t=200/s
(s+10)(t-1)=200
st+10t-s-10=200
s*200/s+10*200/s-s-10=200 plug 200/s for every t in the above equation.
200+2000/s-s-10=200
2000/s-s-10=0
-s^2-10s+2000=0 multiply both sides by s to eliminate the fraction.
s^2+10s-2000=0 multiply both sides times -1
(s+50)(s-40)=0
s can't be a negative number.
s=40 mph
Check:
at 40 mph it takes 5 hrs to go 200 mi
at 50 mph it takes 1 hr less
you had the right answer all the time and didn't know it!
Ed