Question 224529
Start with the distance formula: {{{d = r*t}}} where d = distance, r = rate/speed, and t = time of travel.
For the train:
{{{d[1] = r[1]*t}}} Substitute d = 120km 
{{{120 = r[1]*t}}} Rewrite this as:{{{highlight_green(t = 120/r[1])}}} and substitute into the equation for {{{d[2]}}}.
For the plane:
{{{d[2] = r[2]*t}}} Notice that t (time) is the same in both cases. Substitute d = 336km and {{{r[2] = 3r[1]-10}}}
{{{336 = (3r[1]-10)*t}}} Substitute, from above, {{{highlight_green(t = 120/r[1])}}}
{{{336 = ((3r[1])-10)(highlight_green(120/r[1]))}}} Multiply both sides by{{{r[1]}}}
{{{336*r[1] = ((3r[1])-10)*120)}}} perform the indicated multiplication on the right side.
{{{(336)*r[1]) = 360r[1]-1200}}} Add 1200 to both sides.
{{{1200+336r[1] = 360r[1]}}} Subtract {{{336r[1]}}} from both sides.
{{{1200 = 24r[1]}}} Divide both sides by 24.
{{{50 = r[1]}}} and {{{r[2] = 3(50)-10}}} 
{{{r[1] = 50}}}km/hr. and
{{{r[2] = 140}}}km/hr.
The train is going 50km/hr. and the plane is going 140km/hr.