# Motion

Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist.
Distance between the two cities is 37 km.

Determine the (same) speed of cyclists and walker.

Result

v1 =  17.9 km/h
v2 =  4.5 km/h

#### Solution:

$37= v_1 \cdot \dfrac{ 35+71} { 60} + v_2\cdot \dfrac{ 71} {60} \ \\ 37 = v_1 \cdot \dfrac{ 35+71+8-10} { 60} + v_2 \cdot \dfrac{ 71+8 }{60} \ \\ \ \\ 2220 = 106 v_1 + 71 v_2 \ \\ 2220 = 104 v_1 + 79 v_2 \ \\ \ \\ v_1 = 17.9 \ \text{ km/h }$
$v_2 = 4.5 \ \text{ km/h }$

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