at the beginning of a walk Roberto and Juanita are 33 miles

at the beginning of a walk, Roberto and Juanita are 3.3 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they walk towards each other, they meet in one hour. what are their speeds?

Solution

Distance between Roberto and Juanita is 3.3 miles

let the spped of Roberta is \"x\"

and speed of Juanita is \"y\"

If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours

this means Roberto speed is greater then Juanita

and Roberto has to walk an extra 3.3 miles as he is behind Juanita

Both of them travelled for 11 hrs

distance convered by Roberto = speed X Time

                                                 = 11x

distance convered Juanita = speed X Time

                                                 = 11y

11x -11 y =3.3             // as Roberta has to travel an extra of 3.3 miles

x - y = 0.3                     (1)

now they walk towards each other and they meet each other in an hour

distance convered by Roberto = speed X Time

                                                 = 1x        = x

distance convered by Juanita = speed X Time

                                                 = 1y     =   y

x + y = 3.3       (2)        // as they were 3.3 miles apart

adding (1) and (2) we get

2x = 3.6

x = 1.8 miles/hr (Roberto speed)

using (1)

x-y =0.3

1.8 -y=0.3

y=1.5 miles /hr