Question 178070
The distance is the same going up and down
{{{d = r[u]*t[u]}}}
{{{d = r[d]*t[d]}}}
given:
{{{r[u] = 4}}}km/hr
{{{r[d] = 6}}}km/hr
{{{t[u] + t[d] = 3}}}hrs
{{{d = 4*t[u]}}}
{{{d = 6*t[d]}}}
I can set the right sides equal to eachother
{{{4*t[u] = 6*t[d]}}}
{{{t[u] = (3/2)*t[d]}}}
And, since
{{{t[u] + t[d] = 3}}}
{{{(3/2)*t[d] + t[d] = 3}}}
{{{3t[d] + 2t[d] = 6}}}
{{{5t[d] = 6}}}
{{{t[d] = 6/5}}}hrs
and
{{{t[u] = (3/2)*t[d]}}}
{{{t[u] = (3/2)*(6/5)}}}
{{{t[u] = 9/5}}}hrs
The uphill trip took 1 hr and 4/5 of an hr, or
1 hr and 48 minutes
check:
{{{d = r[u]*t[u]}}}
{{{d = 4*(9/5)}}}
{{{d = 36/5}}}
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{{{d = r[d]*t[d]}}}
{{{d = 6*(6/5)}}}
{{{d = 36/5}}}
The distances are equal as they should be, and
{{{6/5 + 9/5 = 3}}}, the total time is 3 hrs