marina can bicycle 19.5 miles in the same time it takes her to run 6 miles she bikes 9 miles per hour faster than she runs at what speed marina run

4 miles per hour

Step-by-step explanation:

So we have bike speed, b, and run speed, r. We also have an amount of time t where running that amount of time gets 6 miles, while biking that same time gets 19.5. Let's write these out as equations.

rt = 6

bt = 19.5

We are also told that b is 9 more than r so writing that out is b = 9 + r. So it's basically a system of equations.

rt = 6

bt = 19.5

b = 9 + r

Since we have b = 9 + r let's replace b with that in bt = 19.5

rt = 6

(9 + r) t = 19.5

b = 9 + r

With rt = 6 we can get that r = 6/t, so we can plug hat into (9 + r) t = 19.5

rt = 6

(9 + 6/t) t = 19.5

b = 9 + r

Expanding (9 + 6/t) t = 19.5 will get us an equation to solve for t

rt = 6

9t + 6 = 19.5

b = 9 + r

So let's solve for t in 9t + 6 = 19.5

rt = 6

t = (19.5 - 6) / 9 = 1.5

b = 9 + r

Now we can plug this new value for t into rt = 6 to find r. I'm just gonna write that part since this will get us the answer.

rt = 6

r*1.5 = 6

r = 4

So she runs at 4 miles per hour