Flying against the wind, Lisa made the flight from Reno in 3 h with a steady airspeed of 400km/h. Returning later with a tail wind that had doubled in magnitude, she landed 225 km beyond the starting point in 3 h. What was the original wind speed? How far from Reno did she begin the trip?
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To find the original wind speed and the distance from Reno, we need to use the concept of relative velocities.
Let's denote the speed of the wind as "w" km/h.
When flying against the wind, Lisa's effective speed will be her airspeed minus the speed of the wind. So, in this case, her effective speed is 400 km/h - w km/h.
When flying with the wind, Lisa's effective speed will be her airspeed plus the speed of the wind. So, in this case, her effective speed is 400 km/h + w km/h.
We are given that Lisa made the flight from Reno in 3 hours with a steady airspeed of 400 km/h when flying against the wind. So, the distance she traveled can be calculated by multiplying her effective speed by the time: distance = (400 km/h - w km/h) * 3 h.
Similarly, we are given that when Lisa returned with a tailwind that had doubled in magnitude, she landed 225 km beyond the starting point in 3 hours. So, the distance she traveled can be calculated by multiplying her effective speed by the time: distance = (400 km/h + 2w km/h) * 3 h.
We can set up the following equations based on the above information:
(400 km/h - w km/h) * 3 h = distance from Reno
(400 km/h + 2w km/h) * 3 h = distance from Reno + 225 km
We can solve these equations using the method of substitution.
First, let's solve the first equation for the distance:
(400 km/h - w km/h) * 3 h = distance from Reno
1200 km/h - 3w km = distance from Reno
Next, substitute the second equation into the first equation:
(400 km/h + 2w km/h) * 3 h = distance from Reno + 225 km
(1200 km/h + 6w km) = distance from Reno + 225 km
Now, plug in the value of distance from Reno from the first equation into the second equation:
(1200 km/h + 6w km) = 1200 km/h - 3w km + 225 km
1200 km/h + 6w km = 1200 km/h - 3w km + 225 km
Simplify the equation:
9w km = -225 km
w = -25 km/h
Since wind speed cannot be negative, the original wind speed is 25 km/h.
To find the distance from Reno, we can substitute the value of w into the first equation:
1200 km/h - 3w km = distance from Reno
1200 km/h - 3(25 km/h) = distance from Reno
1200 km/h - 75 km/h = distance from Reno
1125 km = distance from Reno
So, Lisa began the trip 1125 km from Reno.