SOLUTION: I need help with this word problem: Alex can run 26 miles in 6 hours, Bethany can run 26 mies in 5 hours and carol can run 26 miles in 4 hours. If they start together and each run

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Question 171829: I need help with this word problem:
Alex can run 26 miles in 6 hours, Bethany can run 26 mies 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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F6t + 26%2F5t + 26%2F4 = 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%2F37
t = 123%2F37 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