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?

1 Answer
Apr 27, 2018

=>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")