Question 166796
You can use: {{{d = rt}}} for this problem, where:
d = distance traveled.
r = rate (speed) of travel.
t = time taken to travel distance d at a speed of r.
For the car, r = 90 km/h.
For the train, r = 75 km/h
{{{d[c] = 90(t-2)}}} (t-2 because the car takes 2 hours less than the train).
{{{d[t] = 75t}}} The distance is the same for each, so...
{{{d[c] = d[t]}}}
{{{90(t-2) = 75t}}}
{{{90t-180 = 75t}}} Subtract 75t from both sides.
{{{15t-180 = 0}}} Add 180 to both sides.
{{{15t = 180}}} Divide both sides by 15.
{{{t = 12}}} Now substitute this into either one of the two distance equations.
For the car:
{{{d[c] = 90(t-2)}}} Substitute t = 12.
{{{d[c] = 90(12-2)}}}
{{{d[c] = 90(10)}}}
{{{d[c] = 900}}}km.
For the train:
{{{d[t] = 75t}}} Substitute t = 12.
{{{d[t] = 75(12)}}}
{{{d[t] = 900}}}km.
The towns are 900 km. apart.