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