Let w represent Lizette's walking speed. Then her running speed is w+6. The relationship between speed, time, and distance is ...
distance = speed × time
Lizette ran for 1.5 hours, then walked for 3 hours. Her total distance is ...
(w+6)·1.5 + w·3 = 18
4.5w + 9 = 18 . . . . . simplify
4.5w = 9 . . . . . . . . . subtract 9
w = 2 . . . . . . . . . . . .divide by 4.5
Lizette's walking speed is 2 mph; her running speed is 8 mph.
Answer:
Walking speed = 2 mph.
Running speed = 8 mph.
Step-by-step explanation:
Let her walking speed be x mph, then her running speed is x + 6 mph
Speed = distance / time. Take the first 1 1/2 hours:
x + 6 = y / 1.5 where y = distance travelled in that time
rewriting:
x + 6 = 2y / 3...........(1)
And the last 3 hours:
x = z / 3.......... (2) where z = distance travelled in that time.
Also we have the equation:
y + z = 18..........(3)
Substitute x = z/3 into equation (i):
z/3 + 6 = 2y/3
Multiply through by 3:
z + 18 = 2y
2y - z = 18 ............(4)
y + z = 18..........(3) Adding these 2 equations:
3y = 36
y = 12 miles,
So z = 18 - 12 = 6 miles.
Now find the value of x:
From equation (2):
x = z/ 3
= 6/3
= 2 mph.
Therefore running speed = 2 + 6 = 8 mph.
