Question 238860
I write 2 equations, 1 for each trip
{{{d[1] = r[1]*t[1]}}}
{{{d[2] = r[2]*t[2]}}}
given:
{{{d[1] = 56}}} mi
{{{d[2] = 56}}} mi
{{{r[2] = r[1] + 8}}} mi/hr
{{{t[2] = t[1] - 1/6}}} (10 min is 1/6 hr)
------------------
given:
{{{d[1] = r[1]*t[1]}}}
(1) {{{56 = r[1]*t[1]}}}
and
{{{d[2] = r[2]*t[2]}}}
{{{56 = (r[1] + 8)*(t[1] - 1/6)}}}
------------------
(2) {{{56 = r[1]*t[1] + 8t[1] - (1/6)*r[1] - 4/3}}}
Substitute (1) in (2)
{{{56 = 56 + 8t[1] - (1/6)*r[1] - 4/3}}}
Subtract {{{56}}} from both sides
{{{8t[1] - (1/6)*r[1] = 4/3}}}
Multiply both sides by {{{6}}}
{{{48t[1] - r[1] = 8}}}
and, from (1)
{{{48*56/r[1] - r[1] = 8}}}
{{{2688/r[1] - r[1] = 8}}}
Multiply both sides  by {{{r[1]}}}
{{{2688 - (r[1])^2 = 8r[1]}}}
{{{(r[1])^2 + 8r[1] - 2688 = 0}}}
Use quadratic equation
 {{{r[1] = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 8}}}
{{{c = -2688}}} 
{{{r[1] = (-8 +- sqrt( 8^2-4*1*(-2688) ))/(2*1) }}}
 {{{r[1] = (-8 +- sqrt( 64 + 10752 ))/2 }}}
 {{{r[1] = (-8 +- sqrt( 10816 ))/2 }}}
{{{r[1] = (-8 + 104)/2}}}
{{{r[1] = 96/2}}}
{{{r[1] = 48}}} (the negative answer is impossible)
{{{r[2] = r[1] + 8}}}
{{{r[2] = 48 + 8}}}
{{{r[2]= 56}}}
The speed on the return trip is 56 mi/hr
check answer:
(1) {{{56 = r[1]*t[1]}}}
{{{56 = (r[1] + 8)*(t[1] - 1/6)}}}
-----------------------
{{{56 = 48*t[1]}}}
{{{t[1] = 1.167}}} hr (1 hr 10 min)
and
{{{56 = (48 + 8)*(t[1] - 1/6)}}}
{{{56 = 56*(t[1] - 1/6)}}}
{{{1 = t[1] - 1/6}}}
{{{6 = 6t[1] - 1}}}
{{{6t[1] = 7}}}
{{{t[1] = 1.167}}} hr
OK