A wildfire burned a large area of a forest. A ranger reported the approximate amount of forest burned.
1 answer:
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We can set it up like this, where <em>s </em>is the speed of the canoeist:
To make a common denominator between the fractions, we can multiply the whole equation by s(s-5):
![s(s-5)[\frac{18}{s} + \frac{4}{s-5} = 3] \\ 18(s-5)+4s=3s(s-5) \\ 18s - 90+4s=3 s^{2} -15s](https://tex.z-dn.net/?f=s%28s-5%29%5B%5Cfrac%7B18%7D%7Bs%7D%20%2B%20%5Cfrac%7B4%7D%7Bs-5%7D%20%3D%203%5D%20%5C%5C%2018%28s-5%29%2B4s%3D3s%28s-5%29%20%5C%5C%2018s%20-%2090%2B4s%3D3%20s%5E%7B2%7D%20-15s)
If we rearrange this, we can turn it into a quadratic equation and factor:
Technically, either of these solutions would work when plugged into the original equation, but I would use the second solution because it's a little "neater." We have the speed for the first part of the trip (9 mph); now we just need to subtract 5mph to get the speed for the second part of the trip.
The canoeist's speed on the first part of the trip was 9mph, and their speed on the second part was 4mph.
To make a common denominator between the fractions, we can multiply the whole equation by s(s-5):
If we rearrange this, we can turn it into a quadratic equation and factor:
Technically, either of these solutions would work when plugged into the original equation, but I would use the second solution because it's a little "neater." We have the speed for the first part of the trip (9 mph); now we just need to subtract 5mph to get the speed for the second part of the trip.
The canoeist's speed on the first part of the trip was 9mph, and their speed on the second part was 4mph.
Answer:
The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.
Step-by-step explanation:
We use the following relation to solve this question:
In which v is the velocity, d is the distance, and t is the time.
Chastain will kick the ball from 18 yards away from the goal at 120 miles per hour.
Since the velocity is in miles per hour, the distance has to be in yards.
Each yard has 0.000568182 miles, so the ball will be kicked from 18*0.000568182 = 0.0102 miles.
This means that
How many seconds does the goalkeeper have to react, dive, and reach the ball before it crosses the goal line?
We have to find t, first in hours. So
An hour has 3600 seconds. So
3600*0.000085 = 0.306.
The goalkeeper has 0.306 seconds to react, dive, and reach the ball before it crosses the goal line.