Question 187282
Jogging:
{{{d[j] = r[j] * t[j]}}}
Walking:
{{{d[w] = r[w] * t[w]}}}
given:
{{{d[j] = 10}}} mi
{{{d[w] = 10}}} mi
{{{r[j] = r[w] + 2.5}}} mi/hr
{{{t[j] + t[w] = 6}}} hr
{{{t[j] = 6 - t[w]}}} hr
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Jogging:
{{{10 = (r[w] + 2.5)* (6 - t[w])}}}
{{{10 = 6r[w] + 15 - r[w]*t[w] - 2.5t[w]}}}
{{{10 = 6r[w] + 15 - 10 - 2.5t[w]}}}
(1){{{5 = 6r[w] - 2.5t[w]}}}
Walking:
{{{10 = r[w]*t[w]}}}
{{{t[w] = 10/r[w]}}}
Substitute this in (1)
(1) {{{5 = 6r[w] - 2.5*(10/r[w])}}}
multiply both sides by {{{r[w]}}}
(1) {{{5r[w] = 6*(r[w])^2 - 25}}}
(1) {{{6*(r[w])^2 - 5r[w] - 25 = 0}}}
Use quadratic formula to solve for {{{r[w]}}}
Then find {{{t[w]}}}, then find {{{r[j]}}}