Question 149897
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={{{x^2+10x}}}
{{{(200x)/(x^2+10x)=(200x+2000)/(x^2+10x)-((x^2+10x)/(x^2+10x))}}}


Subtract on the right
{{{(200x/(x^2+10x))=((200x-2000-x^2-10)/(x^2+10x))}}}


Eliminate the denominator.
Subtract 200x from both sides


{{{0=2000-x^2-10x}}}

Reorder the right side
{{{0=-x^2-10x+2000}}}


Take out a ngeative one
{{{0=-1(x^2+10x-2000)}}}


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


Solve
x=-50
x=40


since speed can't be negative, x=40, so


40 mph