Question 186895
It's not real clear, but I assume the whole trip
takes 1 hr.
Let {{{t[1]}}} = time for the portion on flat ground
Let {{{d[1]}}} = distance for the portion on flat ground
Let {{{t[2]}}} = time for uphill portion
Let {{{d[2]}}} = distance for the uphill portion
Let {{{t[3]}}} = time for downhill portion
Let {{{d[3]}}} = distance for the downhill portion
given:
(1) {{{t[1] + t[2] + t[3] = 1}}} hr
(2) {{{d[1] = 9*t[1]}}}
(3) {{{d[2] = 6*t[2]}}}
(4) {{{d[3] = 18*t[3]}}}
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What I need to find is {{{d = d[1] + d[2] + d[3]}}}
Rewrite (2),(3) and (4) like this:
(2) {{{t[1] = d[1]/9}}}
(3) {{{t[2] = d[2]/6}}}
(4) {{{t[3] = d[3]/18}}}
Add the 3 equations
{{{d[1]/9 + d[2]/6 + d[3]/18 = t[1] + t[2] + t[3]}}}
{{{d[1]/9 + d[2]/6 + d[3]/18 = 1}}}
Write the left side with {{{18}}} as denominators
{{{2*d[1]/18 + 3*d[2]/18 + d[3]/18 = 1}}}
If {{{d[1] = 3}}},
and {{{d[2] = 2}}},
{{{d[3] = 6}}}
The left side is {{{18/18 = 1}}}
{{{d = d[1] + d[2] + d[3] = 3 + 2 + 6}}}
{{{3 + 2 + 6 = 11}}} mi
It is 11 miles between houses
check answer:
(2) {{{t[1] = d[1]/9}}}
(2) {{{t[1] = 1/3}}}
(3) {{{t[2] = d[2]/6}}}
(3) {{{t[2] = 1/3}}}
(4) {{{t[3] = d[3]/18}}}
(4) {{{t[3] = 1/3}}}
(1) {{{t[1] + t[2] + t[3] = 1}}} hr
(1) {{{1/3 + 1/3 + 1/3 = 1}}} hr