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Solve Problems of Direct Variation

One day Emily’s drive to work takes 20 minutes, and she averages 30mph. The next day, her drive only takes 15 minutes.

What is her average speed that day?

t=20 min
r=30 mph

distance = rate x time ( d=r x t )

d= $\frac{30 miles}{hr} \cdot \frac{20 min}{1} \cdot \frac{1hr}{60 min}$

d= $\frac{600 miles}{60}$ =10 miles

t=15 min=?

d=10 miles

d=r x t

$\frac{1}{t} \cdot d = r \cdot t \frac{1}{2}$

$\frac{d}{t}=r$

$\frac{10 miles}{1} \cdot \frac{1}{15 min} = r$

$\frac{10 miles}{1} \cdot \frac{1}{15 min} \cdot \frac{60 min}{1 hr} = \frac{600 miles}{15 hrs}$ =40 mph