<PRE><B>Question 532320</B>
A cyclist and a jogger start from a town at the same time and head for a destination 19 mi away. 
The rate of the cyclist is twice the rate of the jogger. The cyclist arrives 1.9 h before the jogger.
 Find the rate of the cyclist.
:
let r = the rate of the jogger
then
2r = rate of the cyclist
:
Write a time equation, time = dist/speed
:
jogger time - cyclist time = 1.9 hrs
{{{19/r}}} - {{{19/(2r)}}} = 1.9
multiply by 2r, results:
2(19) - 19 = 2r(1.9)
38 - 19 = 3.8r
19 = 3.8r
r = {{{19/3.8}}}
r = 5 mph is the rate of the jogger
then
2(5) = 10 mph is the rate of the cyclist
:
:
Check this find the actual time of each
19/5 = 3.8 hrs
19/10= 1.9 hrs
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time dif: 1.9 hrs</PRE>