An executive flew in the corporate to a meeting in a city 1500 km away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 km to go. The airspeed of the plane was 600 km/h. How fast was the wind blowing (assuming that the wind direction was parallel to the flight path and constant all day.)?
Please show work...
Please show us your thinking and problems if you have any.
well i got this so far:
total d = 1500 km
total time to get to destination = t(subscript)1 which is also equal to time taken to travel 1200 km back home.
Then I used d=rt formula,
I tried 1500 = 600 (t(subscript)1)
t(subscript)1=2.5hrs
2.5hrs =1200 km on return flight
1200r (2.5)
r = 480km/h
1500 = 480 t(subscript)2.
that meant 600 - 480 would be 120 km/h but when i checked my answer, it said that the answer is 66 2/3 km/h... i am confused... PLZ HELP!!!
66 2/3 is correct.
You would want to denote the unknown by a variable name, say v for velocity of wind.
The question stated that the time to travel 1500 km (with the wind) is the same as that required to travel 1200 km back (against the wind).
Can you express the previous paragraph in terms of the wind velocity, v, the air speed of 600 km/h and the distances 1500 and 1200?
If you can, solve it and you should get your required answer of 66 2/3. If not, post again.
sry, I don't understand :[...
"The question stated that the time to travel 1500 km (with the wind) is the same as that required to travel 1200 km back (against the wind). "
Time to traval to destination
= Distance / velocity
= 1500 / (600 + v)
Time to return (part of the way)
= Dostance / velocity
= ...
Equate the two, since they are equal and solve for v.
Can you take it from here?
Oh... hold opn, let me try it!!! if I don't get it, I'll try to post what I did! if i do, then thanx!!
THANK YOU SO MUCH!!!!
I am sure you can. If not, post anyway. If I don't reply tonight, it will be tomorrow.
To find out how fast the wind was blowing, we can use the concept of relative speed.
Let's denote the speed of the wind as 'w' km/h.
During the outbound flight, the effective ground speed of the plane (combination of airspeed and wind speed) would be 600 km/h + w km/h.
Since the distance traveled during the outbound flight was 1500 km, the time taken can be calculated by dividing the distance by the ground speed:
Time = Distance / Speed
Time = 1500 km / (600 km/h + w km/h)
During the return flight, the same amount of time was taken. The distance remaining was 300 km, and the effective ground speed would be 600 km/h - w km/h (since the plane is flying in the opposite direction of the wind).
Using the same formula:
Time = Distance / Speed
Time = 300 km / (600 km/h - w km/h)
Since the time taken during both flights is the same, we can equate the two expressions:
1500 km / (600 km/h + w km/h) = 300 km / (600 km/h - w km/h)
Now we can solve this equation to find the value of 'w', which represents the speed of the wind.
First, cross-multiply the equation:
1500 km * (600 km/h - w km/h) = 300 km * (600 km/h + w km/h)
900000 km * km/h - 1500 km * w km/h = 180000 km * km/h + 300 km * w km/h
Now, simplify the equation:
900000 km * km/h - 180000 km * km/h = 1500 km * w km/h + 300 km * w km/h
720000 km * km/h = 1800 km * w km/h
Finally, divide both sides of the equation by 1800 km/h:
w = (720000 km * km/h) / (1800 km/h)
Simplifying:
w = 400 km/h
Therefore, the wind speed was 400 km/h.