Calculating Wind Speed for City A to City B Trip

[fubag]

City A lies directly west of City B. When there is no wind Captain Dare A. Devil makes a round trip of 6000 km between the two in 10 hours in his airplane while traveling at same speed up and down. Once a strong steady wind was blowing from west to east, and the round trip took him 12 hours. How fast was the wind blowing?


Ok...

So to start, I found the average velocity with no wind to be 600 km/hr.

Then, with the wind, his average velocity fell to 500 km/hr...

Since the wind is blowing west to east, his first trip towards City A must've been slower than his returning trip. So to find the speed of the wind, how do I determine this?

 

[fubag]

any help?

 

[m2003]

To determine the speed of the wind, we can use the concept of relative velocity. The relative velocity of the plane with respect to the wind would be the difference between its velocity with no wind and its velocity with the wind. In this case, it would be 600 km/hr - 500 km/hr = 100 km/hr.

Now, since the wind is blowing from west to east, it would have a negative velocity in the frame of reference of the plane. This means that the wind is acting against the plane's motion, slowing it down. So, we can say that the wind is causing a decrease in velocity of 100 km/hr.

To calculate the actual speed of the wind, we need to consider the distance and time taken for the trip with the wind. We know that the round trip with the wind took 12 hours, so the time taken for one leg of the trip (either from City A to City B or from City B to City A) would be 6 hours.

Using the formula distance = velocity x time, we can calculate the distance covered by the plane in one leg of the trip with the wind:

Distance = 500 km/hr x 6 hr = 3000 km

Since the distance between City A and City B is 6000 km, this means that the plane traveled 3000 km from City B to City A and 3000 km from City A to City B.

Now, since we know the distance and the time taken for one leg of the trip with the wind, we can calculate the actual speed of the wind using the same formula:

Wind speed = Distance / Time = 3000 km / 6 hr = 500 km/hr

Therefore, the wind speed is 500 km/hr blowing from west to east.

In conclusion, the strong steady wind blowing from west to east had a speed of 500 km/hr, causing a decrease in the plane's velocity by 100 km/hr and resulting in a longer round trip time of 12 hours instead of the usual 10 hours.