Aimey runs four times faster than she walks. If a trip took her 45 minutes and she spent 15 of these minutes walking 3km, how far did Aimey run?
Answers
Step-by-step explanation:
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Answer:
Aimey then ran 3km and walked 3km during his journey.
Step-by-step explanation:
We start with the following variables:
r: Aimey's running speed (in km/h)
w: Aimey's walking speed (in km/h)
We know that Aimey runs four times faster than she walks, so we can say:
r=4w
We also know that the entire journey took 45 minutes or 0.75 hours. Meanwhile, Aimey spent 15 minutes or 0.25 hours walking 3 km. We can use the distance formula:
distance = speed x time
To find the distance Aimey has traveled, we need to subtract the distance traveled from the total distance:
distance travelled = total distance - distance travelled
distance travelled = (r x 0.5) - (Width x 0.25)
distance travelled = (4w x 0.5) - (w x 0.25)
running distance = 1.5W
To calculate w we can use the equation x^2 + 1/x^2 = 119 from the previous question:
week^2 + 1/week^2 = 119/16
w^4 + 1 = 119/16 * w^2
16w^4 + 16 = 119w^2
16w^4 - 119w^2 + 16 = 0
If we solve this quadratic equation with the quadratic formula, we get:
w^2 = 0.0504 or w^2 = 4
Since Aimey's walking speed cannot be negative, we can take the positive square root and say: w=2km/h
The distance traveled by Aimey is therefore:
distance traveled = 1.5W = 3km
Aimey then ran 3km and walked 3km during his journey.
Learn more about quadratic equation :
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