SOLUTION: Dennis can swim at a speed of 4 mph. He runs at 9 mph, and he bikes at 22 mph. At a triathlon competition he completed the 68 mile race in 4.5 hours. He spent the same time swimmin

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Question 875265: Dennis can swim at a speed of 4 mph. He runs at 9 mph, and he bikes at 22 mph. At a triathlon competition he completed the 68 mile race in 4.5 hours. He spent the same time swimming as running. How many miles did he complete for each of the 3 parts of the race?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Dennis can swim at a speed of 4 mph. He runs at 9 mph, and he bikes at 22 mph.
At a triathlon competition he completed the 68 mile race in 4.5 hours.
He spent the same time swimming as running.
How many miles did he complete for each of the 3 parts of the race?
:
let t = the times he swam and he ran
let b = time he biked
:
Write a distance equation (dist = speed * time)
4t + 9t + 22b = 68
13t + 22b = 68
:
Write a time equation
2t + b = 4.5
b = -2t + 4.5
:
replace b with (-2t+4.5) in the distance equation
13t + 22(-2t+4.5) = 68
13t - 44t + 99 = 68
-31t = 68 - 99
-31t = -31
t = -31/-31
t = + 1hr swimming and running
then
4.5 - 2(1) = 2.5 hrs biking
Find the distance for each event
4*1 = 4 mi
9*1 = 9 mi
22*2.5 = 55 mi biking
:
:
Check this: 4 + 9 + 55 = 68 mi