Question

Jackie runs and rides her bike. She runs 6 miles an hour. She bikes 18 miles an hour. Last week she ran and bikes a total of 216 miles. It took her 16 hours. How many hours did Jackie run and bike last week. Show your work

Answer 1

Answer: she bikes for 10 hours and runs for 6

Step-by-step explanation: suppose that x equals the amount of hours she runs and y equals the amount of hours she bikes.

6x+ 18y=216

x+y=16

(This is your system of equations)

(Starting with the second equation, x+y=16)

y=-x +16 (move x to the other side by transposition)

Now that you have something that equals Y you plug it in to the other equation:

6x+18(-x+16)=216

(Start solving)

6x-18x+288=216 (used distributive property)

-12x+288=216 (Combine like terms)

-12x=-72 (use transposition again)

x=6 (divide to get x by itself)

Now you plug in the value of x into your equation for the value of “y”, y=-x+16,

Y=-6+16 (plugged in the value of x)

Y=10 (solved the equation -6+16)