Question 1009462
Let the original speed be {{{s( mil/h)}}}. 

distance: 
{{{d=st}}}=>{{{10mil=st}}}
time: {{{t=10/s}}}

{{{d=(s+10)t}}}=>{{{25mil=st}}}
time: {{{t=25/(s+10)}}}

if time {{{t=45min}}}=>{{{t=(45/60)h}}}=>{{{t=0.75h}}}

then we have:

{{{10/s + 25/(s+10) = 0.75}}}


{{{10(s+10) /s(s+10)  + 25/(s+10) = 0.75}}}


{{{((10s+100)  + 25s)/s(s+10) = 0.75}}}


{{{(10s+100 + 25s)= 0.75*s(s+10) }}}


{{{100 + 35s= 0.75(s^2+10s) }}}


{{{100 + 35s= 0.75s^2+7.5s }}}


{{{0= 0.75s^2+7.5s-35s-100}}}


{{{ 0.75s^2-27.5s-100=0}}}..........use quadratic formula


{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{s = (-(-27.5) +- sqrt((-27.5)^2-4*0.75*(-100) ))/(2*0.75) }}} 


{{{s = (27.5 +- sqrt(756.25+300 ))/1.5 }}}


{{{s = (27.5 +- sqrt(1056.25 ))/1.5 }}}


{{{s = (27.5 +- 32.5)/1.5 }}}


we need only positive solution, speed cannot be negative value


{{{s = (27.5 + 32.5)/1.5 }}}


{{{s = 60/1.5 }}}


{{{highlight(s = 40mph)}}}-> original speed