Question 110384
They leave at the same time and collide at the same time, so
If I write{{{t = d[A]/r[A]}}} and {{{t = d[B]/r[B]}}}, then
t is the same for both, and I can write {{{d[A]/r[A] = d[B]/r[B]}}}
and {{{r[A] = 60}}}, {{{r[B] = 50}}}, so
{{{d[A]/60 = d[B]/50}}}
And I know {{{d[A] + d[B] = 100}}}, so I can say
{{{d[B] = 100 - d[A]}}}
Now I have {{{d[A] / 60 = (100 - d[A]) / 50}}}
{{{50*d[A] = 60(100 - d[A])}}}
{{{50*d[A] = 6000 - 60*d[A]}}}
{{{110*d[A] = 6000}}}
{{{d[A] = 54.5454}}}
{{{t = d[A] / r[A]}}}
{{{t = 54.5454 / 60}}}
{{{t = .90909}}}hrs
{{{.90909}}}hrs x {{{60}}}min/hr = {{{54.5454}}}min
{{{.5454}}} min x {{{60}}}sec/min = 32.7272 sec
So, the cars will collide in 54 min 33 sec approximately