Question

Chantal bicycles at a speed of 20 miles per hour and has already riden 45 miles when Trisha begins cycling. Trish bicycles at a speed of 35 miles per hour.
How do you write and solve a system of equations for the given situation?

Answer 1

Answer:

Chantal and Trisha will have both traveled 105 miles in 20 minutes.

Step-by-step explanation:

$y$ is distance in miles, $x$ is time in hours.

The two equations are:

$y = \frac{20}{x} + 45$

$y = \frac{35}{x}$

Set them equal to each other and solve for x:

$\frac{35}{x} = \frac{20}{x} + 45$

$\frac{35}{x} - \frac{20}{x} = 45$

$\frac{35-20}{x} = 45$

$\frac{15}{x} = 45$

$x = \frac{15}{45} = \frac{1}{3} hours = 20 minutes$

Plug that back into the equations to confirm this $x$ gives the same $y$:

$y = \frac{20}{1/3} + 45 = 105 miles$

$y = \frac{35}{1/3} = 105 miles$