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A cyclist travels 20 miles in the same amount of time it takes a hiker to walk 6 miles. The rate of the cyclist is 7 mph faster than the rate of the hiker. Find the rate Of the cyclist.

Answer :

Answer:

The speed of the cyclist is 10 miles per hour .

Step-by-step explanation:

Given as :

The distance cover by cyclist = [tex]D_1[/tex]= 20 miles

The distance cover by biker =  [tex]D_2[/tex] = 6 miles

The speed of biker = [tex]S_2[/tex] = s  mph

The speed of cyclist = [tex]S_1[/tex]= 7 + s  mph

The time taken by both cyclist and biker =  t hour

Now. Distance = Speed × Time

So,  [tex]D_1[/tex] =   [tex]S_1[/tex] × t

Or, 20 = s × t

Or, t = [tex]\frac{20}{7+s}[/tex]             .....1

And ,

[tex]D_2[/tex] =   [tex]S_2[/tex] × t

or, 6 = s t              

Or,  t = [tex]\frac{6}{s}[/tex]  ....2

From Eq  1 and 2

I.e [tex]\frac{20}{7+s}[/tex] = [tex]\frac{6}{s}[/tex]

Or, 20 s = 6 ( 7 + s )

Or, 20 s - 6 s = 42

Or, 14 s = 42

∴   s = [tex]\frac{42}{14}[/tex]

I,e s = 3 miles per hour

So, The speed of biker = [tex]S_2[/tex] = s = 3 miles per hour

And The speed of cyclist = [tex]S_1[/tex]= 7 + s = 7 + 3= 10 miles per hour

Hence The speed of the cyclist is 10 miles per hour . Answer

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