Answer:
Kyla walked 2 miles and jogged 9 miles
Step-by-step explanation:
Let the distance Kyla walked be x
and the distance Kyla jogged be y
Since the trail is 11-mile long, then
x + y = 11
Now, from the question,
Her walking speed is 4 mi/h and her jogging speed is 6 mi/h
Let the time spent to walk be t₁ and the time spent to jog be t₂
From
Distance = Speed × Time
Then, the distance walked x is
x = 4 mi/h × t₁
and the distance jogged y is
y = 6 mi/h × t₂
From the question, Kyla takes 2 hours to go from the beginning to the end of the trail, that is
t₁ + t₂ = 2 hours
∴t₁ = 2 - t₂
Since
x + y = 11, then we can write that
(4 mi/h × t₁) + (6 mi/h × t₂) = 11
But t₁ = 2 - t₂
Then,
(4 mi/h × t₁) + (6 mi/h × t₂) = 11; becomes
(4 mi/h × (2 - t₂)) + (6 mi/h × t₂) = 11
8 - 4t₂ + 6t₂ = 11
2t₂ = 11 - 8
2t₂ = 3
t₂ = 3/2
t₂ = 1.5 hours
This is the time spent to jog
Then, from t₁ = 2 - t₂
t₁ = 2 - 1.5
t₁ = 0.5 hour
This is the time spent to walk
Now, For the distance Kyla walked, x
x = 4 mi/h × t₁
x = 4 mi/h × 0.5
x = 2 miles
Hence, she walked 2 miles
and for the distance Kyla jogged, y
y = 6 mi/h × t₂
y = 6 mi/h × 1.5
y = 9 miles
Hence, she jogged 9 miles
