<PRE><B>Question 159792</B>
two automobiles travel at the rate of 50kph and 30kph respectively. the faster travels 2 hours more than the other and goes 140 kilometers farther. find the distance traveled by each.
:
Let d = distance traveled by the slow car
then
(d+140) = distance traveled by the fast car
:
:
Write a time equation; time = {{{dist/speed}}}
:
Fast car time - 2hrs = slow car time
{{{((d+140))/50}}} - 2 = {{{d/30}}}
Multiply equation by 150 to get rid of the denominators, results:
3(d + 140) - 2(150) = 5d
:
3d + 420 - 300 = 5d
:
120 = 5d - 3d
d = {{{120/2}}}
d = 60 km traveled by the slow car
:
60 + 140 = 200 km traveled by the fast car
:
:
Check the solutions; find the times of each car
200/50 = 4 hrs
60/30 =  2 hrs
-----------------
differ = 2 hrs 
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