Question

Lizette is training for a marathon. At 7:00 she left her house and ran until 8:30, then she walked until 11:30. She covered a total distance of 18 miles. Her running speed was six miles per hour faster than her walking speed. Find her running and walking speeds in miles per hour.

Answer 1

Walking speed = 2 mph.

Running speed = 8 mph.

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.

Answer 2

• running speed: 8 mph
• walking speed: 2 mph

Explanation:

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.