# d =rt problem with two variables

#### 316matrix

##### New member
The problem: June rides her bike 3 mph slower than Kim. June takes 84 minutes longer to ride 64 miles than Kim does. What is each person's speed in mph?

I built this structure for each

J: (r-3)(t+1.4)=64
K: (r)t=64

I solved for t in Kim's and substituted into June's.....like this...

(r-3)(64/r+1.4)=64

I then solved and got r = 13.306...

DId I do it right? I dont know if this is the right answer. It checks ok, but I figure that it is beucause it is the correct solution for the equation. But I dont know if the equation is CORRECT for the problem.

#### Dr.Peterson

##### Elite Member
First, in order to check the work, I had to determine the definition of each variable. It's a very good idea to write that down:
• r = Kim's speed (in mph)
• t = Kim's time (in hours)
Knowing that, your equations are good. Your answer, including units, is that Kim rides at 13.3 miles per hour. You also didn't fully answer the question, which asks for both speeds; June's is 10.3 mph.

Next, we can check your answer, not in your equations (in case they were wrong), but in the words of the problem. Here's how:

We find that Kim's time is t = 64/13.306 = 4.81 hours.

Now if June takes 84 minutes longer than Kim, that's 4.81 + 84/60 = 6.21 hours. Does she go 64 miles? Yes, 10.3*6.21 = 63.963 which is close enough to 64, considering our rounding.

Good work. By the way, there are many other ways to write equations for the problem, and other ways to solve your system; but you way is a very good one.

#### 316matrix

##### New member
Thx Dr P 