Danny and Erica are 3km apart on a straight road. They set out to walk uniformly at the same time. If they walk in an opposite direction, they will meet after 24 minutes. If they walk in the same direction, Danny will catch up to Erica after 6 hours. Find each Individual's speed in km/h.
I'm fine with solving the equation, it's just setting it up which confuses me :L Thanks for any help in advanced.
Where are the steps
Hey, sorry for the late reply. This is what I got:
Danny = 4km/h
Erica = 3.5km/h
i got
Erica= 4km/h
Danny= 4.5km/h
Well, let's start by setting up the equations to solve this problem.
Let's say Danny's speed is represented by "D" km/h and Erica's speed is represented by "E" km/h.
When they walk in opposite directions, their speeds add up, so their relative speed will be D + E km/h. Since they meet after 24 minutes (which is 24/60 = 0.4 hours), the total distance they cover in that time will be (D + E) * 0.4 km.
Therefore, the equation we can set up is: (D + E) * 0.4 = 3.
Now, when they walk in the same direction, Danny will catch up to Erica. In this case, Danny's speed will be faster, so we can subtract their speeds to find the relative speed, which would be D - E km/h. Since they meet after 6 hours, the total distance they cover in that time will be (D - E) * 6 km.
Therefore, the equation we can set up is: (D - E) * 6 = 3.
Now, we have a system of two equations:
(D + E) * 0.4 = 3
(D - E) * 6 = 3.
Solving these equations will give us the values of D and E, which represent Danny and Erica's speeds, respectively.
To solve this problem, let's set up the equations using the information given.
Let's assume Danny's speed is represented by 'D' km/h and Erica's speed is represented by 'E' km/h.
When they walk in opposite directions, their speeds will add up. So, the equation we can set up is:
(D + E) * 24/60 = 3 km (since they meet after 24 minutes)
Simplifying this equation, we get:
(D + E) * 2/5 = 3 km
Now, let's consider when they walk in the same direction. Danny will catch up to Erica, which means the relative speed between them will be D - E (Danny's speed minus Erica's speed).
The distance covered in 6 hours (360 minutes) will be the same for both of them:
(D - E) * 6 = 3 km
Now we have a system of equations:
(D + E) * 2/5 = 3
(D - E) * 6 = 3
Simplifying the first equation, we get:
2D + 2E = 15
And the second equation remains the same.
To solve this system of equations, you can use various methods, such as substitution or elimination.
Let's use the elimination method to solve for D:
Multiplying the first equation by 3, we get:
6D + 6E = 45
Subtracting the second equation from the first equation, we get:
6D + 6E - 6D + 6E = 45 - 3
12E = 42
Dividing both sides by 12, we find:
E = 3.5 km/h
Now, substitute the value of E back into any equation to solve for D. Let's use the first equation:
2D + 2(3.5) = 15
2D + 7 = 15
Subtracting 7 from both sides:
2D = 8
Dividing both sides by 2, we find:
D = 4 km/h
Therefore, Danny's speed is 4 km/h and Erica's speed is 3.5 km/h.
let Danny's speed be d km/h
let Erica's speed by e km/h
If they walk towards each other .... 24 min = 2/5 hr,
(2/5)d + (2/5)e = 3
It they walk in the same direction ... clearly Danny walks faster
6d - 6e = 3
solve the two equations, let me know what you get