Question 242751
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Basic Eqn :  <font color=blue>Speed = Distance / Time </font>


Remember, Rachel Speed should be 50 mi/hr ---> {{{S[1]}}}


After travelling 30 miles in <font color=red>t</font> time ----> {{{S[2]}}}, she increased by 15mi/hr -----> {{{S[3]}}}


Putting the scenario into eqn:
{{{S[1]=S[2]+S[3]}}} ----------> Working Eqn


{{{50(mi/hr)=30(mi/t)+15(mi/hr)}}}
{{{(50-15)(mi/hr)=30(mi/t)}}}
{{{(35(mi/hr))(t)=30mi}}} --->{{{cross(35(mi/hr))(t)/cross(35(mi/hr))=30cross(mi)/35(cross(mi)/hr)}}}
{{{red(t=0.857hr)}}} ---> subst. to {{{S[2]}}}


So, her speed for the 1st 30 miles = {{{30mi/0.857hr=red(35(mi/hr))}}}, ANSWER


Check, go back Working Eqn:
{{{50(mi/hr)=35(mi/hr)+15(mi/hr)}}}
{{{50(mi/hr)=50(mi/hr)}}}


Thank you,
Jojo</font>