Question 149544
200 miles
x speed
y time


200/x=y


200/(x+10)=y-1


Plug in y in the second equation
200/(x+10)=200/x-1


Common denominator on the right side x
200/(x+10)=200/x-x/x


Subtract the numerators
200/(x+10)=(200-x)/x


Cross multiply
200x=-x^2+190x+2000


Subtract 200x from both sides
0=-x^2-10x+2000


Take out negative one
0=-1(x^2+10x-2000)


Factor
0=-1(x+50)(x-40)


Set each equal to zero and solve
(x+50)=0
x=-50

(x-40)=0
x=40


Speed can't be negative, so x=40.


Original speed: 40 mph