Answer:
Kayla: 6 mph
Andrea: 11 mph
Step-by-step explanation:
Let x represent Kayla's speed.
We have been given that Andrea travels 5 mph faster than Kayla, so Andrea's speed would be [tex]x+5[/tex] miles per hour.
We are also told that 7 hours they are 119 miles apart.
[tex]\text{Distance}=\text{Speed}\cdot\text{Time}[/tex]
Distance covered by Kayla in 7 hours would be [tex]7x[/tex] and distance covered by Andrea in 7 hours would be [tex]7(x+5)[/tex].
Since both are travelling in opposite direction, so we will add both the distances to find total distance as:
[tex]\text{Total distance}=7x+7(x+5)[/tex]
[tex]119=7x+7(x+5)[/tex]
[tex]119=7x+7x+35[/tex]
[tex]119=14x+35[/tex]
[tex]119-35=14x+35-35[/tex]
[tex]84=14x[/tex]
[tex]x=\frac{84}{14}[/tex]
[tex]x=6[/tex]
Therefore, Kayla is travelling at a rate of 6 miles per hour.
Andrea's speed would be [tex]x+5\Rightarrow 6+5=11[/tex]
Therefore, Andrea is travelling at a rate of 11 miles per hour.
