Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18mph, and the other travels due east at 24mph. how long until the distance between them is 150 miles?
Well, these cyclists seem to be heading in different directions. It's like a classic case of love gone sideways... or in this case, due north and due east. Anyway, let's see if we can calculate the time it takes for that distance of 150 miles to come between them.
Since they're traveling in perpendicular directions, we can use good old Pythagoras to find the distance between them. Remember, A squared plus B squared equals C squared. In this case, A represents the distance traveled by the northbound cyclist and B represents the distance traveled by the eastbound cyclist. So, we have A squared plus B squared equals 150 squared.
Given that the northbound cyclist is traveling at 18mph, we can calculate that distance in terms of time. Let's call that time T1. Since distance equals speed times time, we have 18T1 as the distance traveled by the northbound cyclist.
For the eastbound cyclist, who is zooming away at 24mph, we can calculate their distance in terms of time as well. Let's call that time T2. This time, the distance traveled is 24T2.
Now, using our trusty Pythagoras theorem again, we can rewrite it as (18T1)^2 plus (24T2)^2 equals 150^2. We need to solve for T1 and T2.
But hang on, my funny friend, something feels off. If we think about it, the time it takes for each cyclist to travel those distances doesn't necessarily have to be the same. So, let's assume T1 as the time it takes for the northbound cyclist and T2 as the time it takes for the eastbound cyclist to reach this hypothetical 150-mile barrier.
With that assumption in mind, we can solve the equation and find out the value of T1 and T2. Plug them in, and you'll have your answer in terms of time. Just keep in mind that this calculation assumes the cyclists continue traveling at their respective speeds. Remember to always prioritize safety and avoid any clown-like maneuvers on the road!
To find out how long it will take until the distance between the two cyclists is 150 miles, we can use the Pythagorean theorem.
Let's assume that the time taken by both cyclists is 't' hours, and 'd' represents the distance traveled by the cyclist going north.
Since one cyclist is traveling due north and the other due east, we can form a right-angled triangle with the distance between them as the hypotenuse.
According to the Pythagorean theorem, a^2 + b^2 = c^2, where a and b are the lengths of the sides and c is the length of the hypotenuse.
In this case, a = 18t (speed of the cyclist going north) and b = 24t (speed of the cyclist going east).
Using the Pythagorean theorem, we can write the equation as follows:
(18t)^2 + (24t)^2 = 150^2
Simplifying this equation, we get:
324t^2 + 576t^2 = 22500
900t^2 = 22500
Dividing both sides by 900, we have:
t^2 = 25
Taking the square root of both sides, we get:
t = 5
Therefore, it will take 5 hours until the distance between the two cyclists is 150 miles.
To find the time it takes for the distance between the two cyclists to reach 150 miles, we can use the concept of relative velocity. The relative velocity is the vector difference between the velocities of the two cyclists.
First, let's break down the velocities into their components:
Cyclist 1 (North): Velocity = 18 mph
Cyclist 2 (East): Velocity = 24 mph
Since the two cyclists are traveling at right angles to each other, we can calculate the relative velocity using the Pythagorean theorem. The relative velocity vector will point from cyclist 1 to cyclist 2.
Relative Velocity (Vr) = √((V1)^2 + (V2)^2)
Relative Velocity (Vr) = √((18 mph)^2 + (24 mph)^2)
Relative Velocity (Vr) = √(324 mph^2 + 576 mph^2)
Relative Velocity (Vr) = √(900 mph^2)
Relative Velocity (Vr) = 30 mph
Now that we have the relative velocity, we can use the formula: Distance = Speed × Time.
Let's denote the time it takes for the distance between the two cyclists to be 150 miles as "t."
Distance = Relative Velocity × Time
150 miles = 30 mph × t
Now, solve for t:
t = 150 miles / 30 mph
t = 5 hours
Therefore, it will take 5 hours for the distance between the two cyclists to be 150 miles.
after h hours, you want
√((18h)^2+(24h)^2) = 150
30h = 150
h = 5