Question

Two tourists left two towns simultaneously, the distance between which is 38 km, and met in 4 hours. What was the speed of each of the tourists, if the first one covered 2 km more than the second one before they met?

Answer 1

`=>v_1 =5 "km"/"hr"`

`=>v_2 = 4.5 "km"/"hr"`

Explanation:

Let `d_1` and `d_2` be the distances traveled in `"km"` by each of the tourists.

We can write the total distance traveled as:

`d_"tot" = d_1 + d_2 = 38`

We are told directly that the first tourist travels more than the second tourist:

`d_1 = d_2 + 2`

We use these two equations to find the distance each tourist covered.

`(d_2 + 2) + d_2 = 38`

`2d_2 + 2 = 38`

`d_2 + 1 = 19`

`d_2 = 18`

Substituting back to find `d_1`:

`d_1 = d_2 + 2 = 18+2 = 20`

So we have found `d_1 = 20 " km"` and `d_2 = 18 " km"`.

We know that each tourist traveled for `t = 4 " hr"`. Velocity is defined as distance per unit time, so we can compute the velocities using the time and distances we found earlier.

`v_1 = d_1/ t = 20/4 = color(blue)(5 "km"/"hr")`

`v_2 = d_2/t = 18/4 = color(blue)(4.5 "km"/"hr")`