Question 1058008
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Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction 
the faster would have overtaken the slower in 5 hours. Find their cycling speeds.
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<pre>
Moving toward each other:

{{{(50/60)*s[1] + (50/60)*s[2]}}} = 25,   which is the same as

{{{s[1]+s[2]}}} = {{{25*(60/50)}}},   or

{{{s[1]+s[2]}}} = 30  {{{km/h}}}.         (1)



Moving in one direction:

{{{25 + 5*s[2]}}} = {{{5*s[1]}}},   which is the same as

25 = {{{5*(s[1]-s[2])}}},   or

{{{s[1]-s[2]}}} = {{{25/5}}}= 5 {{{km/h}}}.      (2)

where {{{s[1]}}} is the faster' speed and {{{s[2]}}} is the slower' speed, in {{{km/h}}}.



Rewrite (1) and (2) as the system:

{{{s[1]+s[2]}}} = 30,        (1')
{{{s[1]-s[2]}}} =  5.        (2')


Add the two equations (1') and (2'). You will get

{{{2*s[1]}}} = 35  --->  {{{s[1]}}} = 17.5 {{{km/h}}}.

Then {{{s[2]}}} = 30 - 17.5 = 12.5 {{{km/h}}}


<U>Answer</U>.  Faster 17.5 {{{km/h}}}; slower 12.5 {{{km/h}}}.
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