Question

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 1

16 mph

Explanation:

You should first form equations related to this information

Given,Tamara can go 4 mph faster than her sister, Samantha

Lets take speed to ride a bike for Samantha to be= x mph

The speed to ride a bike for Tamara will be= x+4 mph

To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara

Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour

Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence

Time taken by Samantha

`=(80)/(x)`

Time taken by Tamara

`=(80)/(4+x)`

Equation for difference in time

`=(80)/(x) -(80)/(4+x) =1`

Solve the equation for difference in time to get value of x which is samantha speed

`=(80)/(x) -(80)/(x+4) =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0`

Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320

x=(-b±√b²-4ac)÷2a

x=(-4±√4²-4×1×-320)÷2×1

`x=(-4+/-√(4^2-4*1*-320) )/(2) \\\\\\x=(-4+/-√(1296) )/2\\\\\\x=(-4+36)/(2) =(32)/(2) =16`

Samantha speed is 16 mph