Answer:
The rate of the slower cyclist is
[tex] 22\frac{4}{5}km/h[/tex]
and that of the faster cyclist is
[tex]27 \frac{4}{5}km/h[/tex]
Step-by-step explanation:
We let x be the rate of the slower cyclist
[tex]rate \times time = distance[/tex]
From the question, the distance between the two towns is 253 and the time taken for the two cyclist to meet is 5 hours
so we can write the equation
[tex]5x + 5(x + 5) = 253[/tex]
We simplify to get the value for x
[tex] \implies5x + 5x + 25 = 253[/tex]
[tex]\implies10x = 253 - 25[/tex]
[tex]\implies10x = 228 [/tex]
[tex]\implies x =22 \frac{4}{5} [/tex]
Hence the rate of the slower cyclist is
[tex]22 \frac{4}{5} km/h[/tex]
and that of the rate faster cyclist is
[tex]27 \frac{4}{5}km/h[/tex]
