Answer:
Shreya's average speed was 65 kilometers per hour.
Step-by-step explanation:
Let the average speed of Shreya be r.
Recall that the distance d traveled is given by the equation:
[tex]\displaystyle d = rt[/tex]
Where r is the speed and t is the time (in this case hours).
After one hour, when Jill left, Shreya would have already traveled:
[tex]\displaystyle d = r(1) = r\text{ km}[/tex]
Only r kilometers.
Jill caught up in five hours. Hence, Shreya would've traveled another:
[tex]\displaystyle d = r(5) = 5r\text{ km}[/tex]
Therefore, in the six hours, Shreya traveled a total distance of:
[tex]\displaystyle r + 5r = 6r\text{ km}[/tex]
Jill drove at a speed of 13 km/hr faster than Shreya's speed. She drove for five hours. Hence, Jill's total distance traveled is represented by:
[tex]\displaystyle d = (r + 13)\cdot 5 = 5(r+13)[/tex]
This must be equivalent to Shreya's total distance traveled as Jill caught up to her. Hence:
[tex]\displaystyle 5(r+13) = 6r[/tex]
Solve for r:
[tex]\displaystyle \begin{aligned} 5(r+13) &= 6r \\ 5r + 65 &= 6r \\ r&= 65\end{aligned}[/tex]
In conclusion, Shreya's average speed was 65 kilometers per hour.
