Question 344588
Rate*Time=Distance
.
.
{{{R*t=D}}}
1.{{{R[p]*t=270}}}
2.{{{R[f]*t=200}}}
3.{{{R[p]=R[f]+14}}}
Substitute eqs. 1 and 2 into eq. 3,
From eq. 1,
{{{t=270/R[p]}}}
From eq. 2,
{{{t=200/R[f]}}}
Set them equal to each other,
{{{270/R[p]=200/R[f]}}}
{{{270*R[f]=200*R[p]}}}
{{{R[f]=(20/27)*R[p]}}}
Substitute into eq. 3,
{{{R[p]=(20/27)*R[p]+14}}}
{{{R[p](1-20/27)=14}}}
{{{R[p](27/27-20/27)=14}}}
{{{R[p](7/27)=14}}}
{{{R[p]=(27*14)/7}}}
{{{highlight(R[p]=54)}}}mph
Then from eq. 3,
{{{highlight(R[f]=40)}}}mph