TWO PLANES WHICH APART, FLY TOWARDS EACH OTHER. THEIR SPEEDS DIFFER BY 60 MILES PER HOUR. THEY PASS EACH OTHER AFTER 5 HOURS. FIND THEIR SPEEDS.
approach speed = v + v+60 = 2 v+60
d = rate * time = (2v+60)(5) = 10 v + 300
unfortunately we were not given d, their distance apart so I am faced with a problem or a typo.
To find the speeds of the two planes, let's break down the problem and use a system of equations.
Let's denote the speed of the slower plane as x miles per hour. Since the speeds of the two planes differ by 60 miles per hour, the speed of the faster plane would be x + 60 miles per hour.
Now, we know that the two planes fly towards each other and pass each other after 5 hours. To find their speeds, we can use the formula:
distance = speed * time
For the slower plane, its distance traveled would be (x miles per hour) * (5 hours), which is 5x miles.
For the faster plane, its distance traveled would be (x + 60 miles per hour) * (5 hours), which is 5(x + 60) miles.
Since the two planes are flying towards each other, the sum of their distances traveled would be the total distance between them when they pass each other. Therefore, we can set up the following equation:
5x + 5(x + 60) = total distance
Simplifying the equation, we get:
5x + 5x + 300 = total distance
Combining like terms:
10x + 300 = total distance
Since their total distance is not provided, we cannot solve for the actual values of their speeds. However, we can still find a relationship between the speeds of the two planes.
If we divide both sides of the equation by 10, we get:
x + 30 = total distance / 10
So, the difference in their speeds (60 miles per hour) is equal to the total distance between them divided by 10.
In conclusion, the speeds of the two planes cannot be determined without knowing the total distance between them. However, we established a relationship that the difference in their speeds is equal to the total distance divided by 10.