Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?

Answer:16 mphStep-by-step explanation:You should first form equations related to this informationGiven,Tamara can go 4 mph faster than her sister, SamanthaLets take speed to ride a bike for Samantha to be=  x mphThe speed to ride a bike for Tamara will be= x+4 mphTo cover a distance of 80 miles, Samantha takes 1 hour longer than TamaraIntroduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hourHere time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, henceTime taken by Samantha[tex]=\frac{80}{x}[/tex]Time taken by Tamara[tex]=\frac{80}{4+x}[/tex]Equation for difference in time[tex]=\frac{80}{x} -\frac{80}{4+x} =1[/tex]Solve the equation for difference in time to get value of x which is samantha speed[tex]=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0[/tex]Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320x=(-b±√b²-4ac)÷2ax=(-4±√4²-4×1×-320)÷2×1[tex]x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16[/tex]Samantha speed is 16 mph