# Algebraic Word Problem: Finding Speed (Math Problem Sample)

Algebraic word problem

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 travelling?

hint:

Let Vivian’s speed be x, then present the information on a diagram and proceed to solve for each.

Algebraic word problem

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 travelling?

Solution

Let Vivian’s speed be x, then present the information as shown in the figure below

Total distance = 136 miles

Total time = 8 hours

Vivian speed = x

Noelle speed = x+5

Distance = Speed × Time

Distance covered by Vivian = 8x

(speed × Time)

Distance covered by Noelle = 8(x+5)

= 8x+40

Total distance = 136

8x + 8x+40 = 135

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