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math question ?
Suppose you have entered and 86 mile biathlon that consist of a run and a bicycle race. during your run, your average velocity is 8 miles per hour, and during your bicycle race, your average velocity is 23 mph. you finish the race in 7 hours. what is the distance to the run? what is the distance of the bicycle race?
2 Answers
- az_lenderLv 71 month agoFavorite Answer
Let t be the time spent running:
8t + 23*(7 - t) = 86 =>
161 - 86 = 15t =>
t = 5 hours.
Ran 40 miles, biked 46 miles.
- ?Lv 71 month ago
Given d = d₁ + d₂ = 86 mi
r₁ = 8 mph r₂ = 23 mph
t₁ = t hrs t₂ = (7-t) hrs
// Use the formula: d = rt.
// We know that r₁t₁ + r₂t₂ = d so
8 mph (t hrs) + 23 mph (7-t) hrs = 86 mi
8t mi + 161 mi - 23t mi = 86 mi
-15t mi = -75 mi
t = 5
so, t₁ = 5 hrs and t₂ = (7-5) hrs = 2hrs
Therefore,
the distance run is d₁ = r₁t₁ = 8 mph (5 hrs) = 40 mi ....................ANS
and
the distance biked is d₂ = r₂t₂ = 23 mph (2 hrs) = 46 mi ..............ANS
