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?
I don't understand any of the responses.
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.
Erica, David, Shawn, or whoever,
Your question has been answered below. If there is a particular part of the response that you don't understand, please let the math teachers know what that is. To simply say you don't understand doesn't give them much to work with.
I am having problems with this part:
add the equations...
33+63)km/time=64km/hr
then time= 96/64 hr (I know this is 1.5)
Now solve for speed of wind in the first equation..
(is it 33km/1.5 =22)
33km/time=32km/hr-speedwind.
I assume you can add the equations.
Then solve for time.
Now to solve for wind speed
33/1.5=32-speedwind
33/1.5 -32=-speedwind
I assume you can solve that.
Thank you I have the answer as 10km/h.
To find the speed of the wind, we need to use the equation Vrg = Vrgs + Vwind. Here, Vrg is the net velocity relative to the ground, Vrgs is the velocity relative to the ground in still conditions, and Vwind is the velocity of the wind.
We are given that Erik can bicycle at a speed of 32 km/h with no wind, so Vrgs = 32 km/h.
Next, we are told that when Erik bicycles against the wind, he can bike 33 km in the same time it takes to bike 63 km with the wind. This gives us the following equations:
33 km / time = 32 km/h - Vwind
63 km / time = 32 km/h + Vwind
To solve for the speed of the wind, we can add the two equations:
(33 km / time) + (63 km / time) = 64 km/h
Simplifying, we get:
96 km / time = 64 km/h
Now, we can solve for the time:
time = 96 km / 64 km/h
Simplifying further, we find:
time = 1.5 hours
Now, we can substitute the time value into the first equation to find the speed of the wind:
33 km / 1.5 hours = 32 km/h - Vwind
Simplifying, we have:
Vwind = 32 km/h - (33 km / 1.5 hours)
Calculating it out, we find:
Vwind ≈ -1 km/h
Since the wind cannot have a negative speed, it implies that there is an error made in the initial problem statement or calculations. Please check the problem again or provide additional information if possible.