Question 175451
For each train:
{{{t = d/v}}}
Given:
For passenger train:
{{{t = 392/v[p]}}}
For freight train:
{{{t = 322/v[f]}}}
(1){{{392/v[p] = 322/v[f]}}}
(2){{{v[p] = v[f] + 20}}}
Substitute for {{{v[p]}}} in (1)
{{{392/(v[f] + 20) = 322/v[f]}}}
Multiply both sides by {{{v[f]*(v[f] + 20)}}}
{{{392v[f] = 322*(v[f] + 20)}}}
{{{392v[f] = 322v[f] + 6440}}}
{{{70v[f] = 6440}}}
{{{v[f] = 92}}} mi/hr
and, since
(2){{{v[p] = v[f] + 20}}}
{{{v[p] = 112}}}mi/hr
check:
For passenger train:
{{{t = 392/v[p]}}}
{{{t = 392/112}}}
{{{t = 3.5}}} hrs
For freight train:
{{{t = 322/v[f]}}}
{{{t = 322/92}}}
{{{t = 3.5}}}hrs
OK