If one plane is flying 40 mph and another plane is flying 100 mph, and they are 200 miles apart and flying directly toward each other, in how long will the planes meet?
To find the time it takes for the planes to meet, we can use the formula: time = distance / speed.
Let's consider the distance traveled by the slower plane, which is flying at 40 mph. Let's call this distance x.
Similarly, the distance traveled by the faster plane, flying at 100 mph, can be represented as 200 - x (as they are 200 miles apart initially).
We can set up the equation: x / 40 = (200 - x) / 100.
By cross-multiplying, we get: 100x = 40(200 - x).
Simplifying this equation leads to: 100x = 8000 - 40x.
Combining like terms, we have: 140x = 8000.
Dividing both sides of the equation by 140, we find: x = 57.14.
So, the slower plane will have traveled approximately 57.14 miles when they meet.
Now, to find the time it takes, we can substitute x = 57.14 into the time formula for the slower plane: time = distance / speed.
The time taken by the slower plane would be: 57.14 miles / 40 mph ≈ 1.43 hours.
Therefore, the planes will meet in approximately 1.43 hours.