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: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 milesThe distance cover by biker =  [tex]D_2[/tex] = 6 milesThe speed of biker = [tex]S_2[/tex] = s  mphThe speed of cyclist = [tex]S_1[/tex]= 7 + s  mphThe time taken by both cyclist and biker =  t hourNow. Distance = Speed × TimeSo,  [tex]D_1[/tex] =   [tex]S_1[/tex] × tOr, 20 = s × tOr, t = [tex]\frac{20}{7+s}[/tex]             .....1And ,[tex]D_2[/tex] =   [tex]S_2[/tex] × tor, 6 = s t              Or,  t = [tex]\frac{6}{s}[/tex]  ....2From Eq  1 and 2I.e [tex]\frac{20}{7+s}[/tex] = [tex]\frac{6}{s}[/tex] Or, 20 s = 6 ( 7 + s )Or, 20 s - 6 s = 42Or, 14 s = 42∴   s = [tex]\frac{42}{14}[/tex]I,e s = 3 miles per hourSo, The speed of biker = [tex]S_2[/tex] = s = 3 miles per hourAnd The speed of cyclist = [tex]S_1[/tex]= 7 + s = 7 + 3= 10 miles per hourHence The speed of the cyclist is 10 miles per hour . Answer