```Question 529309
Let {{{t}}} = minutes spent running
given:
Routine #1
Calories burnt = {{{ 25 + 18t }}}
Routine #2
Calories burnt = {{{ 49 + 14t }}}
------------------------
Let calories burnt = {{{C}}}
The question is:
for what values of {{{t}}} is
{{{ 49 + 14t > 25 + 18t }}}
Subtract {{{ 14t }}} from both sides
{{{ 49 > 25 + 4t }}}
Subtract {{{ 25}}} from both sides
{{{ 24 > 4t }}}
{{{ 6 > t }}}
or, what is the same,
{{{ t < 6 }}}
So, for all values of {{{t < 6 }}} minutes spent running,
The calories burnt using routine #1 are less than
the calories burnt using #2
Here's a plot of routine #1 and #2:
{{{ graph( 400, 400, -1, 7, -5, 150, 18x + 25, 14x + 49 ) }}}
The bottom line is routine #1. You can see that when {{{ t = 0 }}}
{{{ C = 25 }}} as it should, and they meet at {{{t=6}}}```
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