Question 399516
In 6 min, the 1st runner goes {{{5*(1/10) = .5}}} mi
(note that 6 min = 6/60 hr)
Now the 2 runners will run for the same amount of time
with a half-mile headstart for runner #1.
2nd runner:
(1) {{{d = 7t}}}
1st runner:
(2) {{{d - .5 = 5t}}}
Substitute (1) in (2):
(2) {{{7t - .5 = 5t}}}
{{{2t = .5}}}
{{{t = .25}}} hr
It will take the 2nd runner 15 min to catch the 1st
check answer:
{{{d = 7*(1/4)}}}
{{{d = 1.75}}}
and, also,
{{{d - .5 = 5*(1/4)}}}
{{{d = .5 + 1.25}}}
{{{d = 1.75}}}
OK