Question 231990
In this problem, both the car and the truck are traveling
for the same amount of time.
Write separate {{{d = r*t}}} equations for both
given:
{{{t}}} is the same for both
{{{d[c] = d[t] + 72}}}
{{{r[c] = 2*r[t]}}}
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(1) {{{d[c] = r[c]*t}}}
(2) {{{d[t] = r[t]*t}}}
and, rewriting:
(1) {{{d[c] = r[c]*t}}}
(2) {{{d[c] - 72 = (r[c]/2)*t}}}
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Multiply both sides of (2) by {{{2}}}
(2) {{{2d[c] - 144 = r[c]*t}}}
Now substitute (1) in (2)
(2) {{{2d[c] - 144 = d[c]}}}
Subtract {{{d[c]}}} from both sides
(2) {{{d[c] = 144}}} mi
and from 
 {{{d[c] = d[t] + 72}}}
{{{d[t] = d[c] - 72}}}
{{{d[t] = 144 - 72}}}
{{{d[t] = 72}}}
They both travelled for {{{3}}} hrs, so
The car's speed is
{{{144/3 = 48}}} mi/hr
The truck's speed is
{{{72/3 = 24}}} mi/hr