Ginny and Jenna are 20 miles from home. They have one pair of roller skates. Jenna walks 4mph and skates 9mph. Ginny walks 3 mph and skates 8mph. They start for home at the same time.
First, Ginny has the skates and Jenna walks. Ginny skates for a while, then takes the roller skates off and starts walking.When Jenna reaches the roller blades, she puts them on and starts skating home.
If they both start at 4:00 and arrive home at the same time, what time is it when they get home?
My solution,
I assumed that the time that Ginny skates is $a$ hours and walks for $b$ hours. And hence Jenna skates for $b$ hours and walks for $a$ hours. And since total distance covered is 20 for both, I got the following 2 equations.
$ \begin{align} 8a + 3b &= 20 \\ 4a + 9b &= 20 \end{align} $
I solved this system of equations by elimination to get $b = \dfrac{4}{3}$ and $a = 2$, and $a + b = \dfrac{10}{3}$. This doesn't check out with the required solution which is $4$ and arriving at $8$ pm.
I have checked the simultaneous equation, so I have probably made a logic error. Any ideas where I went wrong. Thanks.