Question 162271
{{{d = r*t}}} for both and
{{{t}}} is the same for both
{{{r[h] = r[c] + 60}}}
For helicopter:
{{{630 = r[h]*t}}}
{{{630 = (r[c] + 60)*t}}}
For car:
{{{210 = r[c]*t}}}
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For helicopter:
{{{t = 630 / (r[c] + 60)}}}
For car:
{{{t = 210 / r[c]}}}
The time,{{{t}}} is the same for both, so
{{{630 / (r[c] + 60) = 210 / r[c]}}}
Multiply both sides by {{{r[c]*(r[c] + 60)}}}
{{{630r[c] = 210*(r[c] + 60)}}}
{{{630r[c] = 210r[c] + 12600}}}
{{{420r[c] = 12600}}}
{{{r[c] = 30}}} km/hr
and, since
{{{r[h] = r[c] + 60}}}
{{{r[h] = 90}}} km/hr
The car travels 30 km/hr and the helicopter
trvels 90 km/hr
check:
{{{630 / (r[c] + 60) = 210 / r[c]}}}
{{{630 / (30 + 60) = 210 / 30}}}
{{{63/9 = 21/3}}}
{{{7 = 7}}}
OK