Mark leaves the house for school walking at the rate of 4 km. per hour. Two hours later Kris follows Mark at a walking rate of 6 km. per hour. How long will Kris have to walk to overtake Mark?
Their corresponding distances travelled is the same.
let the time taken by Kris be x hours
then time taken by Mark is x+2 hours
6x = 4(x+2)
solve for x
distance = (rate) (time)
Mark rate is 4 kph
Kris rate is 6 kph
Let the time taken by Kris be x
And Mark be x + 2
Kris = Mark
(rate) (time) = (rate) (time)
(6) (x) = (4) (x+2)
6x = 4(x+2)
6x = 4x + 8
6x – 4x = 8
2x = 8
x = 4 Kris needs 4 hours
To figure out how long Kris will have to walk to overtake Mark, we need to find the time it takes for Kris to catch up with Mark.
Let's assume that Kris catches up with Mark after t hours.
In the first two hours, Mark has already walked a distance of 4 km/hour × 2 hours = 8 km.
By the time Kris starts walking, Mark is 8 km ahead.
Now, let's calculate the distance covered by Kris in t hours while walking at 6 km/hour:
Distance = 6 km/hour × t hours
To catch up with Mark, Kris needs to cover a total distance of 8 km.
Therefore, we can set up the equation:
Distance covered by Kris = Distance covered by Mark + Distance needed to catch up
6t = 8 + 8
6t = 16
Now, divide both sides of the equation by 6:
t = 16/6
t = 2.67 hours
So, Kris will have to walk for approximately 2.67 hours to overtake Mark.
To find out how long Kris will have to walk to overtake Mark, we need to calculate the distance that Mark covers in the time it takes Kris to catch up.
Let's denote the time it takes Kris to catch up as "t" hours.
In the first two hours, Mark walks at a rate of 4 km/h. Therefore, in two hours, Mark covers a distance of 4 km/h * 2 h = 8 km.
Now, let's calculate how far ahead Mark is when Kris starts walking. Since Kris walks at a faster rate than Mark, he closes the gap between them at a speed of 6 km/h - 4 km/h = 2 km/h.
We already know that Mark was 8 km ahead when Kris started walking. Since Kris closes the gap at a rate of 2 km/h, it will take him 8 km / 2 km/h = 4 hours to catch up with Mark.
Therefore, Kris will have to walk for 4 hours to overtake Mark.