Answer:
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
