I'm not quite sure how to set this problem up. This is the first of the entire worksheet and I'm sure if I understand one problem I can finish the rest pretty easily.
The problem states: When there is no wind, Amelia flies her plane from Oklahoma City to San Francisco in exactly 4 hours, at an average speed of 325 mph. If she were flying into a 25-mile-per-hour head wind, how long would the trip take?
distance = rate*time
d= 325 x 4 = 1,300 miles.
If flying into a 25 mph head wind, then the speed is just 325-25 = 300. Plug in d and r and calculate time.
To solve this problem, we need to understand the concept of relative velocity.
When there is no wind, Amelia's plane flies from Oklahoma City to San Francisco in 4 hours at an average speed of 325 mph. This means that the distance between the two cities is calculated as:
Distance = Speed × Time
Distance = 325 mph × 4 hours = 1300 miles
Now, let's introduce the concept of a headwind. A headwind is the wind blowing directly against the direction of travel. In our case, the headwind is 25 mph.
To find out how long the trip would take with a headwind, we need to take the effect of the headwind into consideration. We can do this by subtracting the headwind speed from the plane's speed.
New Speed = Plane's Speed - Headwind Speed
New Speed = 325 mph - 25 mph = 300 mph
Now, we can use the new speed to calculate the time it would take for the trip with the headwind. We can set up a new equation:
Distance = Speed × Time
Using the distance we calculated earlier (1300 miles) and the new speed (300 mph), we can rearrange the equation to solve for time:
Time = Distance / Speed
Time = 1300 miles / 300 mph
Let's do the division to find the time:
Time = 4.33 hours
Therefore, when flying into a 25-mile-per-hour headwind, the trip would take approximately 4.33 hours.