A plane flies with a ground speed of 160 miles per hour if there is no wind. It travels 350 miles with a head wind and in the same time it takes to go 450 miles with a tail wind. Find the speed of the wind.
I'm pretty bad with word problems, but this is how I answered it:
set an equation:
(350)mph / (160-x)mph = (450)mph / (160+x)mph
solved to get x (windspeed)=20
was this the right way to do it? If not, could somebody please explain?
Thanks a bunch.
correct
thanks ya
Yes, you are absolutely correct! Your approach to solving the problem is correct.
Let's break it down step-by-step:
1. Let's assume the speed of the wind is "x" miles per hour.
2. When the plane is flying against the wind (headwind), its effective speed is reduced by the speed of the wind. So, the ground speed is (160 - x) miles per hour.
3. According to the information given, the plane takes the same amount of time to travel 350 miles against the wind as it does to travel 450 miles with the wind.
4. We can set up the following equation using the formula: distance = speed × time:
350 / (160 - x) = 450 / (160 + x)
5. Cross-multiply to get rid of the fractions:
350(160 + x) = 450(160 - x)
6. Simplify and expand:
56000 + 350x = 72000 - 450x
7. Rearrange the equation by bringing all the "x" terms to one side:
350x + 450x = 72000 - 56000
800x = 16000
8. Solve for x by dividing both sides of the equation by 800:
x = 16000 / 800
x = 20
Hence, the speed of the wind is 20 miles per hour. Well done!
Yes, you are on the right track! Let's break it down step by step to see how to solve this problem.
Step 1: Define the variables
Let's define the speed of the wind as "x" (in miles per hour). This means that the plane's speed with a headwind would be 160 - x, and its speed with a tailwind would be 160 + x.
Step 2: Calculate the time.
The time taken to travel a certain distance is equal to the distance divided by the speed. So, for the first scenario with a headwind, the time taken to travel 350 miles is 350 / (160 - x). Similarly, for the second scenario with a tailwind, the time taken to travel 450 miles is 450 / (160 + x).
Step 3: Set up the equation.
We are given that these times are equal, so we can set up the equation:
350 / (160 - x) = 450 / (160 + x)
Step 4: Solve the equation.
To solve this equation, we can start by cross-multiplying:
350(160 + x) = 450(160 - x)
Step 5: Simplify the equation.
Expand and simplify the equation:
56,000 + 350x = 72,000 - 450x
Step 6: Rearrange the equation.
Move all the terms with x to one side:
350x + 450x = 72,000 - 56,000
800x = 16,000
Step 7: Solve for x.
Divide both sides by 800 to solve for x:
x = 16,000 / 800 = 20
So, the speed of the wind is 20 miles per hour.
Your initial intuition and approach were correct! You set up the equation correctly and solved it to find the value of x (the speed of the wind). Well done!