# 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.

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

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