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?

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.

Rewrite the equation for time

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

Using cross multiplication rule.

x = 2.65 mi\hr

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

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