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Pie
2 years ago
14

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?
Mathematics
1 answer:
melomori [17]2 years ago
4 0

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

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