Question 127073
car A: {{{d[a] = r[a]*t[a]}}}
car B: {{{d[b] = r[b]*t[b]}}}
given: {{{t[a] = t[b]}}}
{{{d[a] = 250}}}km
{{{d[b] = 400}}}km
{{{r[a] = r[b] - 30}}} km/hr
putting all this together:
car A: {{{250 = (r[b]- 30)*t}}}
car B: {{{400 = r[b]*t}}}
solve each one for {{{t}}}
{{{t = 250 / (r[b] - 30)}}}
{{{t = 400 / r[b]}}}
Set these equal to eachother
{{{250 / (r[b] - 30) = 400 / r[b]}}}
multiply both sides by {{{r[b]*(r[b] - 30)}}}
{{{250*r[b] = 400*(r[b] - 30)}}}
{{{150*r[b] = 12000}}}
{{{r[b] = 80}}}
{{{r[a] = r[b] - 30}}}
{{{r[a] = 50}}}
The rate of car A is 50 km/hr
The rate of car B is 80 km/hr
check answer
{{{t = 250 / (r[b] - 30)}}}
{{{t = 400 / r[b]}}}
--------------------------
{{{t = 250 / 50}}}
{{{t = 5}}}hrs
{{{t = 400 / 80}}}
{{{t = 5}}}hrs
OK