d Problem 4: 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? | Job Exam Rare Mathematics (JEMrare) - Solved MCQs
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Problem 4: 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?

Problem 4 : 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?

Solution:

<——————Park———————>

——————(136 m)———————

Let speed of Vivian = x m/h

Then according to given information;

Speed of Noelle = (x+5) m/h

Both the persons moved apart in 8 hours!

Now we know that;

\[ Distance=Speed\times Time \]

So, distance travelled by Vivian

\[ =x\times 8=8x m \]

and

distance travelled by Noelle

\[ =(x+5)\times 8=8(x+5) \]

As per given information – total distance travelled apart by both the persons should by 136 m!

That is

\[ Vivian Distance+Noelle Distance=136 \]

or

\[ 8x+8(x+5)=136 \]

or

\[ 8x+8x+40=136 \]

or

\[ 16x+40=136 \]

or

\[ 16x=136-40=96 \]

or

\[ x=\frac{96}{16}=6 \]

or

\[ x=6 m/hr \]

So, Vivian is travelling with speed of 6 miles per hour.

and Noelle is moving with speed= x+5=6+5=11 miles per hour

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