Question 170780
distance equals rate times time
lets call the 1st 150 miles rate=r and time=t
and we will call the last 100 miles rate r-5 and time 10-t
:
150=rt--->t=150/r.....eq 1
100=(r-5)(10-t).......eq 2
:
take value of t from eq 1 and plug it into eq 2
:
100=(r-5)(10-(150/r))--->100=(r-5)((10r-150)/r)...multiply both sides by r
:
100r=(r-5)(10r-150)
:
{{{100r=10r^2-150r-50r+750}}}
{{{10r^2-300r+750=0}}}divide by 10
:
{{{r^2-30r+75=0}}}

r=27.25 and 2.75......throw out the 2.75 rate because r-5 is negative.
so {{{highlight(r=27.25)}}}mph-the original speed of the storm

 *[invoke quadratic "x", 1, -30, 75]