Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 9. km/h due east. Runner B is initially 5.0 km east of the flagpole and is running with a constant velocity of 8.0 km/h due west. How far are the runners from the flagpole when their paths cross?
I did it this way.
time for A to get to the flag pole is t = d/r = 6/9 = 0.667 hour.
time for B to get to the flag pole is t = d/r = 5/8 = 0.625 hour.
That means runner B gets to the flag pole first and will still be running west BEFORE runner A gets to the flag pole. Thus, runner B will run the 5 km + a distance x and runner A will run 6 - x. Setting that up.
Runner A. t = (6-x)/9
Runner B. t = (5+x)/8.
Now set the times equal and solve for x.
(6-x)/9 = (5+x)/8
Their paths will cross at 6 km - x km and 5 km + x km.
x is the distance from the flag pole when their paths cross.
I hope this helps.
is it 0.176
Mate what.
Well, it seems like you've got the math all figured out! But let me give you a more humorous perspective on the situation.
Runner A and Runner B are playing a game of who can get to the flagpole first. Runner A, being the brave soul that they are, decides to start off 6.0 km west of the flagpole, thinking they can catch up by running at a steady pace of 9.0 km/h due east.
Meanwhile, Runner B, who is feeling a tad mischievous, decides to start off 5.0 km east of the flagpole and run at 8.0 km/h due west. It's like a game of cat and mouse!
Now, what happens when their paths cross? It's like a classic meet-cute in a romantic comedy. Runner A, after running for a certain amount of time, realizes that Runner B is not just chasing them for fun, but heading towards the flagpole too. What a plot twist!
As they both continue running, their paths eventually intersect at a certain distance from the flagpole. It's like destiny brought them together, but instead of true love, it's a race!
So, my friend, the question of how far they are from the flagpole when their paths cross is a moment of anticipation. It's the climax of their little "game" and the answer lies in solving the equation you came up with.
I hope my humorous take on the situation brought a smile to your face, even if it didn't provide any additional mathematical insight. Keep up the good work with those equations!
Your approach is correct. To find the distance at which the runners' paths cross, you set the time it takes for each runner to reach the flagpole equal to each other.
Runner A:
t = (6 - x) / 9
Runner B:
t = (5 + x) / 8
Setting these equations equal to each other:
(6 - x) / 9 = (5 + x) / 8
To solve for x, you can cross-multiply:
8(6 - x) = 9(5 + x)
48 - 8x = 45 + 9x
Now, solve for x:
8x + 9x = 48 - 45
17x = 3
x = 3 / 17
Therefore, x is approximately 0.1765 km.
To find the distance at which their paths cross, subtract x from Runner A's initial distance west of the flagpole:
6 km - x
So, the distance at which the runners' paths cross is approximately 5.8235 km from the flagpole.