Question 209589
Each person has their own equation
For Jenna:
{{{d[j] = r[j]*t[j]}}}
For Caleb:
{{{d[c] = r[c]*t[c]}}}
given:
{{{r[j] = 10}}} mi/hr
{{{r[c] = 8}}} mi/hr
{{{t[j] = t[c]}}} hr (I'll call them both {{{t}}})
{{{d[j] = d[c] + .1}}}
Notice that they both start at the same time
and they finish at the same time.
And also, Jenna has to go 1/10 mi further
---------------------
Now I can rewrite their equations
{{{d[j] = r[j]*t[j]}}}
{{{d[c] + .1 = 10t}}}
and
{{{d[c] = r[c]*t[c]}}}
{{{d[c] = 8t}}}
By substitution,
{{{8t + .1 = 10t}}}
{{{2t = .1}}}
{{{t = .05}}} hr
Converting to minutes:
{{{.05*60 = 3}}} min
It will take Jenna 3 minutes to catch him
check answer:
{{{d[c] + .1 = 10t}}}
{{{d[c] = 10*.05 - .1}}}
{{{d[c] = .5 - .1}}}
{{{d[c] = .4}}} mi
and
{{{d[j] = 10t}}}
{{{d[j] = 10*.05}}}
{{{d[j] = .5}}} mi
This shows Caleb has {{{.5 - .4 = .1}}} headstart
OK