# Math Help - Rate Question

1. ## Rate Question

Max runs the first 4km of her training session at 8 km/h. At least how many kilometers must she run at 15 km/h in order to average 12 km/h for the whole session.

2. Hello, begold91!

Max runs the first 4km of her training session at 8 km/h.
At least how many kilometers must she run at 15 km/h
in order to average 12 km/h for the whole session?

Max ran 4 km at 8 km/hr.
. . This took $\frac{4}{8} \,=\,\frac{1}{2}$ hours.
She will run $x$ more km at 15 km/hr.
. . This will take $\frac{x}{15}$ hours.
She will run a total of: $\frac{1}{2} + \frac{x}{15}$ hours.

She will run a total of $x + 4$ km at an average speed of 12 km/hr.
. . Her total time will be: $\frac{x+4}{12}$ hours.

There is our equation! . $\frac{1}{2} + \frac{x}{15}\:=\:\frac{x+4}{12}$

3. You could try several equations.

Since distance/rate=time:

$\frac{4}{8}+\frac{d-4}{15}=\frac{d}{12}$, solve for d.

Since distance = rate*time:

$8(\frac{1}{2})+15(t-\frac{1}{2})=12t$, solve for t to find d.