Question

At the beginning of a? walk, Roberto and Juanita are 4.4 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 1 hour. What are their? speeds?

Answer 1

Let, speeds of Roberto and Juanita be x miles/hour and y miles/hour respectively.

Then by given condition we have,

x*11 = y*11+4.4

11x = 11y+4.4

i.e., 11x-11y = 4.4

i.e., 11(x-y) = 4.4

i.e., x-y = 4.4/11

i.e., x-y = 0.4.................(i)

And, x*1+y*1 = 4.4

i.e., x+y = 4.4................(ii)

Now, adding (ii) with (i) we get, (x-y)+(x+y) = 0.4+4.4

i.e., 2x = 4.8

i.e., x = 4.8/2

i.e., x = 2.4

Putting this in (i) we get,

2.4+y = 4.4

i.e., y = 4.4-2.4

i.e., y = 2

Therefore, speeds of Roberto and Juanita are 2.4 miles/hour and 2 miles/hour respectively.