Answer: Melissa's walking speed is 2mph. Her biking speed is 6mph
Explanation:
Her total distance is 6 miles, because she walks 3 miles, and so the returning distance must also be 3.
Let her cycling speed (in mph) be x
Let her walking speed (in mph) be y
We know that x = y + 4
Since we know that S = D/T:
T = D/S
So her cycling time must be: T = 3/x
and her walking time must be: T = 3/y
since we know that x = y + 4, we can substitute this into her cycling time, and rewrite it as T = 3/y+4
we also know that 3/y+4 + 3/y = 2, because the problem says that the total time taken was 2 hours.
We simply need to solve this equation now:
3/y+4 + 3/y = 2
The LCD for y+4 and y is y² + 4y
so now we have:
(3y/y² + 4y) + (3y+12/y² + 4y) = 2
(6y + 12)/y² + 4y = 2
6y + 12 = 2y² + 8y
2y² + 2y - 12 = 0
Solve this using factoring:
2y² + 2y - 12 = 0
2(y² + y - 6) = 0
(y+3)(y-2) = 0
using ab = 0, then a or b =0:
y = -3, or y = 2
Since speed cannot be negative, our answer is 2 for y. So y, or the walking speed is 2mph. Since x = y + 4, we know that x = 6 mph
Melissa's walking speed is 2mph. Her biking speed is 6mph