Question 202389
Using the distance formula:
{{{d = rt}}} where: d = distance, r = rate (speed), and t = time of travel.
For the trip to Jakarta:
{{{d[1] = r[1]*t[1]}}} Substitute: {{{r[1] = 182}}} and {{{t[1] = t[2]+6}}}
{{{d[1] = (182)(t[2]+6)}}}
For the return trip:
{{{d[2] = r[2]*t[2]}}} Substitute: {{{r[2] = 455}}}
{{{d[2] = 455*t[2]}}}
The distance to Jakarta is equal to the return distance, so...
{{{d[1] = d[2]}}} and so...
{{{(182)(t[2]+6) = 455*t[2]}}} Simplify and solve for {{{t[2]}}}
{{{182*t[2]+1092 = 455*t[2]}}} Subtract {{{182*t[2]}}} from both sides of the equation.
{{{1092 = 273*t[2]}}} Divide both sides by 273.
{{{t[2] = 4}}}hours.
{{{t[1] = t[2]+6}}}
{{{t[1] = 4+6}}}
{{{highlight(t[1] = 10)}}}hours.
Check:
{{{10*182 = 4*455}}}
{{{1820 = 1820}}} OK!