A turbo-jet flies 50 mph faster than a super-prop plane. If a turbo-jet goes 2000 miles in 3 hours less time than it takes the super-prop to go 2800 miles, find the speed of each plane.
I do not understand how to do this at all. Please explain as well as you can! Thanks.
LEt v be the velocity of the turbo plane, then v-50 is the velocity of the slower. Let t be the time for turbo to go 2000 miles, then t+3 is the time for super .
(velocity*time)= distance
(v-50)(t+3)=2800
and
v*t=2000
From the second equation, t=2000/v, put that into the first equation.
(v-50)(2000/v + 3)=2800
multiply both sides by v
(v-50)(2000+3v)=2800v
multiply it all out, gather terms, and use the quadratic equation.
turbo-jet: 400mph
super-prop: 350mph
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the speed of the super-prop plane is "x" mph.
According to the problem, the speed of the turbo-jet is 50 mph faster, so the speed of the turbo-jet plane can be expressed as "x + 50" mph.
Now, let's use the formula "speed = distance / time" to find the time it takes for each plane to travel their respective distances.
For the super-prop plane:
Distance = 2800 miles
Speed = x mph
Time = Distance / Speed = 2800 / x
For the turbo-jet plane:
Distance = 2000 miles
Speed = (x + 50) mph
Time = Distance / Speed = 2000 / (x + 50)
According to the problem, the turbo-jet takes 3 hours less time than the super-prop to cover their respective distances. So, we can set up the equation:
2800 / x - 2000 / (x + 50) = 3
Now, we can solve this equation to find the value of "x" which represents the speed of the super-prop plane. Once we have the value of "x", we can calculate the speed of the turbo-jet by adding 50 to it.
Steps to solve the equation:
1. Multiply both sides of the equation by (x)(x + 50) to eliminate the denominators.
(2800)(x + 50) - (2000)(x) = 3(x)(x + 50)
2. Expand and simplify both sides of the equation:
2800x + 140000 - 2000x = 3x^2 + 150x
3. Combine like terms:
800x + 140000 = 3x^2 + 150x
4. Move all terms to one side of the equation:
3x^2 + 150x - 800x - 140000 = 0
5. Simplify the equation:
3x^2 - 650x - 140000 = 0
Now, you can solve this quadratic equation to find the value(s) of "x" using factoring, completing the square, or the quadratic formula. Once you find the value(s) of "x", you can substitute it back into the equation "x + 50" to find the speed of the turbo-jet plane.