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Two cyclists start at the same point and travel in opposite directions. One cyclist travels 10 kilometers per hour slower than the other. If the two cyclists are 240 kilometers apart after 5 hours, what is the rate of each cyclist?

Respuesta :

Answer:

The speed of First cyclist is 25 kilometers per hour

The speed of second cyclist is 15 kilometers per hour

Step-by-step explanation:

Given as :

The distance between tow cyclist = D = 240 kilometers

The time taken when both apart 240 km = 5 hours

Let the speed of first cyclist = [tex]s_1[/tex] = s kmph

And The speed of second cyclist = [tex]s_2[/tex] = ( s - 10 ) kmph

Let The distance cover by first cyclist =  [tex]d_1[/tex] = x km

And The distance cover by second cyclist =  [tex]d_2[/tex] = ( 240 - x ) km

Now, Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

So, For First cyclist

T = [tex]\dfrac{d_1}{s_1}[/tex]

Or, 5 = [tex]\dfrac{x}{s}[/tex]

Or, x = 5 s        ........1

Now, For Second cyclist

T = [tex]\dfrac{d_2}{s_2}[/tex]

Or, 5 = [tex]\dfrac{240 - x}{s - 10}[/tex]

Or, 240 - x = 5 ( s - 10 )                ....2

Putting The value of x from Eq 1 into Eq 2

I.e 240 - 5 s = 5 ( s - 10 )    

Or, 240 - 5 s = 5 s - 50

Or, 240 + 10 = 5 s + 5 s

or. 250 = 10 s

∴  s = [tex]\dfrac{250}{10}[/tex]

I.e s = 25 kmph

So, The Speed of First cyclist = s = 25 kmph

And The speed of second cyclist = ( s - 10 ) = 25 - 10 = 15 kmph

Hence The speed of First cyclist is 25 kilometers per hour

And The speed of second cyclist is 15 kilometers per hour  Answer