Erik bicycles 32 km/h with no wind. Against the wind he bikes 33 km in the same time it takes to bike 63 km with the wind. What is the speed of the wind?
This school subject is math.
Erik bicycles 32 km/h with no wind. Against the wind he bikes 33 km in the same time it takes to bike 63 km with the wind. What is the speed of the wind?
You have to assume in this case the wind s and assists with the same force, which is not usually true.
Vrg=Vrgs+Vwind
where Vrg is net velocity relative to ground, Vrgs is velocity relative to ground in still conditions, and Vwind is the velocity of the wind.
Vrgs=32
33km/time=32km/hr-Speedwind
63km/time=32km/hr+speed wind.
add the equations...
33+63)km/time=64km/hr
then time= 96/64 hr
Now solve for speed of wind in the first equation..
33km/time=32km/hr-speedwind.
Now solve for speed of wind in the first equation..
33km/time=32km/hr-speedwind.
How do I do that?
To find the speed of the wind, we can use the concept of relative speed.
Let's assume the speed of the wind is "W" km/h.
When Erik is biking against the wind, his effective speed is reduced by the speed of the wind. So his effective speed is (32 - W) km/h.
When Erik is biking with the wind, his effective speed is increased by the speed of the wind. So his effective speed is (32 + W) km/h.
Now, we know that the time taken to bike a certain distance is equal to the distance divided by the speed.
When Erik bikes against the wind, the distance is 33 km and the speed is (32 - W) km/h. So the time taken is 33 / (32 - W) hours.
When Erik bikes with the wind, the distance is 63 km and the speed is (32 + W) km/h. So the time taken is 63 / (32 + W) hours.
Since the times taken for both cases are the same, we can set up an equation:
33 / (32 - W) = 63 / (32 + W)
To solve this equation, we can cross-multiply:
33 * (32 + W) = 63 * (32 - W)
1056 + 33W = 2016 - 63W
Combining like terms:
96W = 960
Dividing both sides by 96:
W = 10
Therefore, the speed of the wind is 10 km/h.