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Answer :
Final answer:
To find the wind speed, two equations are set up based on Jim's known running speed and the distances he runs with and against the wind. Solving these equations yields the wind's rate, which is approximately 5.29 miles per hour.
Explanation:
To determine the rate of the wind, we need to set up two equations using the formula speed equals distance divided by time (s = d/t). Let's denote the wind speed as 'w'. When Jim runs with the wind, his effective speed increases by w, and when he runs against the wind, his effective speed is decreased by w.
With the wind: s + w = 13/t
Against the wind: s - w = 4/t
We are given that Jim's running speed (s) on level ground on a still day is 5 miles per hour. We can set both distances equal to each other since the time taken for both is the same.
(5 + w) × t = 13
(5 - w) × t = 4
By solving these equations, we can find the value of w, the wind speed.
Multiplying the second equation by -1 and adding both equations:
-w = -9/t
Thus, w = 9/t and the equations become:
5t + (9/t) = 13
5t - (9/t) = 4
Now we add both equations:
10t = 17
Therefore, t = 1.7 hours
Substituting t into w = 9/t gives us:
w = 9/1.7 = 5.29 (approximately) miles per hour.
Therefore, the rate of the wind is approximately 5.29 miles per hour.
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Rewritten by : Barada
Answer: the rate of the wind is 2.65 mph
Step-by-step explanation:
Let x represent the speed of the wind.
Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 13 miles with the wind. This means that his total speed with the wind is (5 + x) mph.
Time = distance/speed
Time taken to cover 13 miles would be 13/(5 + x)
In the same amount of time runs 4 miles against the wind. This means that his total speed against the wind is (5 - x) mph. Time taken to cover 4 miles would be 4/(5 - x).
Since both times are the same, it means that
13/(5 + x) = 4/(5 - x)
Cross multiplying, it becomes
13(5 - x) = 4(5 + x)
65 - 13x = 20 + 4x
4x + 13x = 65 - 20
17x = 45
x = 45/17
x = 2.65
