Vivian and Noelle both leave the park at the same time, but in
opposite directions. If Noelle travels 5 mph faster than Vivian and
after 8 hours, they are 136 miles apart, how fast in mile per hour is
each traveling?
Step 3: Solve for mph by using the part “…after 8 hours, they are
136 miles apart…”
8𝑥 + (8𝑥 + 40) = 136 𝑚𝑖𝑙𝑒𝑠
8𝑥 + 8𝑥 + 40 = 136 𝑚𝑖𝑙𝑒𝑠
16𝑥 + 40 = 136 𝑚𝑖𝑙𝑒𝑠
Solution:
16𝑥 = 136 𝑚𝑖𝑙𝑒𝑠 − 40 𝑚𝑖𝑙𝑒𝑠
Step 1: Let,
Vivian’s speed (in mph) = 𝑥
16𝑥 = 96 𝑚𝑖𝑙𝑒𝑠
Noelle’s speed (in mph) = 𝑥 + 5
𝑥=
96
𝑚𝑝ℎ
16
𝑥 = 6 𝑚𝑝ℎ
Distance formula:
Distance = speed × time
Step 4: Find the equivalent speed of Vivian and Noelle
Vivian’s distance = x
𝑥 = 6 𝑚𝑝ℎ
Step 2: Insert values
Vivian’s distance:
𝑥
𝑚𝑖𝑙𝑒𝑠
ℎ𝑜𝑢𝑟
× 8 ℎ𝑜𝑢𝑟𝑠 = 8𝑥 𝑚𝑖𝑙𝑒𝑠
Noelle’s Distance:
(𝑥 + 5)
𝑚𝑖𝑙𝑒𝑠
ℎ𝑜𝑢𝑟
× 8 ℎ𝑜𝑢𝑟𝑠 = (8𝑥 + 40)𝑚𝑖𝑙𝑒𝑠
Noelle’s distance = x+5
𝑥 + 5 = 6 + 5 = 11 𝑚𝑝ℎ
Answer: Vivian travels at a speed of 6 mph while Noelle travels at a
speed of 11 mph.