It will take an hour for plane A to meet plane B which is flying towards it. If, within 45 minutes, the distance between them will be 200 miles, how far apart are they now?
they are d miles apart at the start
Va + Vb = V
V(1) = d
V(3/4) = d-200
d(3/4) = d - 200
200 = d/4
d = 800
To determine how far apart the planes are now, we first need to calculate the relative speed of the two planes. Let's consider the speed of plane A as 'A' and the speed of plane B as 'B'.
Since the planes are flying towards each other, their speeds add up, so the relative speed can be calculated as A + B.
We are given that it will take one hour for the planes to meet, but within 45 minutes, the distance between them will be 200 miles. This means that the planes will meet within 45 minutes, or three-quarters of an hour.
To find the relative speed, we can divide the distance between the planes (200 miles) by the time it takes for them to meet (3/4 hour):
Relative speed = Distance / Time = 200 miles / (3/4) hour
To simplify, we can multiply the numerator by 4 to get rid of the fraction in the denominator:
Relative speed = 200 miles / (3/4) hour = (200 miles * 4) / 3 hour
Now we can calculate the relative speed:
Relative speed = (200 miles * 4) / 3 hour = 800 miles / 3 hour
Therefore, the relative speed of the two planes is 800 miles per 3 hours, which can be simplified to 266.67 miles per hour (rounded to two decimal places).
Since we know the relative speed of the planes, we can set up the equation:
Distance = Relative speed * Time
Let 'd' be the distance between the two planes now. We can rearrange the formula to solve for 'd':
d = Relative speed * Time
Substituting the known values:
d = 266.67 miles/hour * 0 hour
Since the time is 0 hours (as we want to know the distance now), the term with time becomes zero:
d = 0 miles
Therefore, the planes are currently 0 miles apart, meaning they are at the same location.