i need help with algebra

Question

Brian and Tyler drove together for eight hours. So far, they have driven three hundred eight miles. Brian drove the first three hours. Tyler drove the rest of the way at a speed of nineteen less than two times Brian’s speed (in miles per hour). What was Tyler’s average speed?

Answer 1

This problem falls under weighted averages as well as a system of equations. We will use B for Brian's speed and T for Tyler's speed. we know that (B+T)/2 would be the average speed if they drove equal distances, but they didn't so we will have to make a weighted average speed instead. knowing brian drove 3 hours(as stated in the problem and Tyler the remaining (5 hours) we can use this expression for average speed (2B+5T)/8. average speed is also defined by total distance over total time therefore we get another expression 308/8 so we can get the expression (3B+5T)/8 =308/8 this can be simplified to (3B+5T) =308.

There are 2 unknowns so we must create a second equation. However the second part of this word problems compares Tyler's speed with Brian's speed it says that T =2B -19 (19 less than twice B(Brian's speed)) therefore we have our second equation.

We substitute T in our first equation for (2B-19) and we get (3B +5(2B-19))=308 this simplifies to 13B =403 which gives us Brian's speed(B) =31 plugging 31 back into our second equation we find Tyler's speed(T)= 43 miles per hour. if you have additional questions feel free to contact me through Wyzant,