Jim can run 5 miles per hour on level ground on a still day. One windy​ day, he runs 13 miles with the​ wind, and in the same amount of time runs 4 miles against the wind. What is the rate of the​ wind?

Answer :

Answer:

Speed of the wind = 2.65 mi\hr

Step-by-step explanation:

Let x be the speed of wind.

Given:

Jim runs on a still day = 5 mi/hr

Jim runs with the wind = 13 mi

Jim runs against the wind = 4 mi

We need to find the speed of the wind.

Solution:

From the above statement Jim speed with wind (5 + x) and speed against the wind (5 - x).

Using speed formula distance upon time.

[tex]speed = \frac{distance}{time}[/tex]

Rewrite the equation for time

[tex]time = \frac{distance}{speed}[/tex]

From the given statement time for both situation is same. So, we write the time equation for both.

[tex]\frac{13}{(5+x)} =\frac{4}{(5-x)}[/tex]

Using cross multiplication rule.

[tex]13(5-x)=4(5+x)[/tex]

[tex]65-13x=20+4x[/tex]

[tex]65-20=13x+4x[/tex]

[tex]17x=45[/tex]

[tex]x = \frac{45}{17}[/tex]

x = 2.65 mi\hr

Therefore, the speed of the wind is 2.65 mi\hr.

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

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