Question

Two cyclists drive a distance of 15 kilometres. One of the cyclists drives
10km h faster than the other one and arrives at their destination 20 minutes
earlier. What are the speeds of the cyclists?

Answer 1

x = speed of one
10 + x = speed of the other

the one with 10 km/min +x speed got to the destination in 20 minutes so...

15kilometer/20 minutes = 10 km/hr + x

let's convert km/min to km/hr first..

15 km 60 min
---------- x ---------
20 minutes 1 hour

75 km/hr will be the converted value (see calculator)

so...

75 km/hr -10 km/hr = x

65 km/hr = x
x + 10 = 75 km/hr

Answer 2

I used d = r*t
let r be the speed of the slower cyclist, and t be the time for the slower cyclist.

so we have
15 = r*t
15 = ( r + 10) ( t - 20/60) , since the units are km/hr , then 20 min = 20/60 hr

Answer 3

so t = 15/r , and substitute that into second equation
15 = ( r + 10) ( 15/r - 1/3) , solve that