Writing system of equations & rate of change

Question

"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."

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

Answer 1

Let's call the rate and time of the first plane $r_{1}$ and $t_{1}$, respectively. Since we know the journey is 600 miles, we have $600 = r_{1}t_{1}$. Now, let us look at the second plane. We know that the second plane takes 2 hours longer, and it is going 50 mph slower, and it also travels 600 miles, so the two equations we have are:

$600 = r_{1}t_{1}$ and $600 = (r_{1}-50)(t_{1} + 2)$

Answer 2

From your starting point of $d = rt$, we set up an equation for each plane.

Plane 1: It reaches a city that is 600 miles away in T amount of time. It is flying at a speed S.

So its equation is $600 = TS$.

Plane 2: It reaches that same city 2 hours later or T + 2 hours. It is traveling 50 miles slower than Plane 1 or S - 50.

Then it's equation is $600 = (T+2)(S-50)$

Hope that helps.