Algebraic Word Problem: Speed (Math Problem Sample)

Vivian and Noelle both leave the park at the same time but in opposite directions. If Noelle travels five mph faster than Vivian and after 8 hours, they are 136 miles apart. How fast in mile per hour is each traveling?
Vivian and Noelle both leave the park at the same time but in opposite directions. If Noelle travels five mph faster than Vivian and after 8 hours, they are 136 miles apart. How fast in mile per hour is each traveling?

Let Vivian speed be x
Noelle speed = x+5
Total time =8 hours
From law of motion, Distance = Speed × Time
Distance covered by Noelle = (x+5) × 8 hours
= 8(x+5)
= 8x+40
Distance covered by Vivian = 8x
Total Distance from Vivian to Noelle = 136 miles
Therefore (8x+40) + 8x = 136 miles
(8x+40) + 8x = 136
8x+40+8x = 136
16x = 136-40
16x = 96
x = 6
Vivian is travelling at 6 mph.
Noelle speed = x+5 = 6+5 = 11 mph.