Murielle rides her bike to the mall, which is 3 km from her home. She gets a flat tire
and has to walk home. She averages 4 km/h faster riding her bike than walking. Her
total travelling time is 2 hours. Find her walking speed.
Let's assume Murielle's walking speed is "w" km/h.
Given that Murielle rides her bike to the mall, which is 3 km from her home, we can calculate the time it takes for her to ride to the mall using the equation:
(time for riding) = (distance) / (rate for riding)
(time for riding) = 3 km / (w + 4) km/h
Since she has a flat tire and has to walk home, the walking distance is also 3 km. We can calculate the time it takes for her to walk home using the equation:
(time for walking) = (distance) / (rate for walking)
(time for walking) = 3 km / w km/h
Given that her total travelling time is 2 hours, we can write the equation:
(time for riding) + (time for walking) = 2 hours
(3 km / (w + 4) km/h) + (3 km / w km/h) = 2
Now we can solve this equation to find the value of w, her walking speed.
Multiplying both sides of the equation by (w + 4)w, we get:
3w + 12 + 3w + 12w = 2(w + 4)w
Expanding and simplifying:
6w + 12 + 12w = 2w^2 + 8w
Combining like terms and rearranging:
2w^2 - 14w - 12 = 0
Simplifying the equation by dividing by 2:
w^2 - 7w - 6 = 0
Now we can factor this quadratic equation:
(w - 6)(w + 1) = 0
Setting each factor equal to zero:
w - 6 = 0 or w + 1 = 0
Solving for w, we get:
w = 6 or w = -1
Since speed cannot be negative, we ignore the solution w = -1.
Therefore, Murielle's walking speed is 6 km/h.