Respuesta :
Solution :
Given that, A man is walking across a 300 foot long field at the same time his daughter is walking towards him from the opposite end.
Speed of man = 9 feet per second.
Speed of his daughter = 6 feet per second.
To calculate after how many seconds both will, meet we first need to calculate their relative speed.
And as we know that, when two bodies move in opposite direction then
Relative speed = sum of their speed = 6 + 9 = 15 feet per second.
Time taken by both of them to meet some where in the middle of the 300 foot long field
distance =[tex]\frac{300}{2} =150[/tex]
[tex]\Rightarrow Distance\:= speed\times time[/tex]
[tex]\Rightarrow time =\frac{distance}{speed}[/tex]
[tex]\Rightarrow time=\frac{150}{15} =10[/tex]
Hence ,it will take 10 seconds to them to meet somewhere in the middle.
Let distance traveled by father be x feet
then distance traveled by daughter will be 300-x feet
speed = distance / time
and time = distance / speed
Since they both meet at the same time
[tex]\frac{x}{9}=\frac{300-x}{6}[/tex]
cross multiplying gives
[tex]6x= 2700-9x[/tex]
[tex]15x=2700[/tex]
this gives x= 180 feet
So the distance traveled by father is 180 feet
Now time = distance/ speed
So time taken by father = [tex]\frac{180}{9}[/tex] = 20 seconds.
Hence it will take both of them 20 seconds to meet somewhere in the middle.
