Question 134451
Let x = speed walking

Speed running = (x+6)

Time = distance/speed

time = timeRunning + timeWalking
{{{time = (5/(x+6)) +  1/x }}}
{{{time = (5x+ x+6)/(x(x+6)) }}}
{{{(3/4)(x^2 + 6x) = 6x + 6 }}}
{{{3x^2 + 18x = 24x + 24}}}
{{{3x^2 -6x - 24 = 0 }}}
{{{(3x + 6)(x-4) = 0 }}}
x = -2, x = 4

since he can't walk at -2, walking speed must be 4mph
The running is 10mph

Check your answer. He will run 30 minutes at 10mph to cover 5 miles. He will walk 1 mile in 15 minutes. total 6 miles in 45 minutes. Check!