Question 171829
Alex can run 26 miles in 6 hours, Bethany can run 26 miles in 5 hours and carol
 can run 26 miles in 4 hours. If they start together and each run at their
 constant speeds, how long does it take for them to finish a total of 26 miles
 among the three of them?
 express your answer in as a common fraction in simplest form.
:
Let t = time required for the three of them run a total of 26 mi
:
Speed = dist/time
:
Dist = speed * time
:
{{{26/6}}}t + {{{26/5}}}t + {{{26/4}}} = 26
:
Multiply equation by 60 to get rid of the denominators; results:
10(26)t + 12(26)t + 15(26) = 60(26)
:
Simplify, divide equation by 26
10t + 12t + 15t = 60
:
37t = 60
t = {{{60/37}}}
t = 1{{{23/37}}} hrs or 1 hr 37.3 min
:
:
Check on a calc using 1.62 hrs
(26/6)*1.62  + (26/5)*1.62  + (26/4)*1.26 = 25.97 ~ 26 mi