Question

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

Answer 1

Question:

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

Explanation:

Note that Ciara can go 4mph faster than Collen.

Let's take the speed to ride a bike for Collen to be x mph.

The speed to ride a bike for Ciara will be (x + 4) mph

Now, to cover a distance of 80 miles, Collen takes 1 hour longer than Ciara. Applying the kinematics equation for motion at constant speed:

$v=\frac{d}{t}$

where v is velocity, d is distance and t is time, we can solve this equation for the time t:

$t=\frac{d}{v}$

Here time Collen takes to cover a distance of 80 miles in 1 hour is more than that taken by Ciara, hence:

Time taken by Collen:

$t=\frac{80}{x}$

Time taken by Ciara:

$t=\frac{80}{x+4}$

The equation for the difference in time:

$\frac{80}{x}\text{ - }\frac{80}{x+4\text{ }}=1$

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

$x^2+4x\text{ - 320=0}$

Solving the quadratic equation by the quadratic formula where a=1,b=4, and c=-320, we get:

$x=16$

Answer: Colleen's speed is 16 mph.