System of Equations: Solving Rates of Planes 600 Miles Apart

[mathgeek7365]

"Two planes leave a city for another city that us 600 miles away. One of the planes is flying 50 miles per hour faster than the other. The slower plane takes 2 hours longer to reach the city. What is the rate of each plane? Write and solve a system of equations."

My daughter is well aware that d=rt, where d represents distance, r represents rate, and t represents time. She also knows how to solve systems of equations. She is unsure on how to create the system of equations from the information given. She would like some hints as to how to start/she would like some help getting on the right track. Thanks.

 

[soroban]

Hello, mathgeek7365!

"Two planes leave a city for another city that us 600 miles away.
One of the planes is flying 50 miles per hour faster than the other.
The slower plane takes 2 hours longer to reach the city. What is
the rate of each plane? Write and solve a system of equations."

My daughter is well aware that d = rt, where d represents distance,
r represents rate, and t represents time. She also knows how to solve
systems of equations. She is unsure on how to create the system of
equations from the information given.

We will use: $$\; d\,=\,rt \quad\Rightarrow\quad t \,=\,\frac{d}{r}$$

The slower plane flies at $$r$$ mph.
The faster plane flies at $$r\!+\!5$$ mph.

The faster plane flies 600 miles at $$r\!+\!5$$ mph.
This takes:$$\:\tfrac{600}{r+5} \:=\:t$$ hours.

The slower plane flies 600 miles at $$r$$ mph.
This takes: $$\:\tfrac{600}{r} \:=\:t+2$$ hours.

There are the two equations.