Conversion Question

Question

A heavy rain fell on a city for 26 minutes, at a rate of 3.9mm/hr. If the area of the city is 244km^2, how many gallons of water fell on the city that day?

Answer 1

First convert minutes into hours. So we have: $26 min = \frac{26}{60}h = \frac{13}{30}h$

Now multiply the time by the rate to find how much rain did fall.

$\frac{13}{30} \times \frac{39}{10} = \frac{507}{300}mm$.

If rain wouldn't go underground and it stayed above ground then the depth of the "pool" would be $\frac{507}{300}mm$. Now multiply that by the area to get volume. First we'll try to convert everything in meters, because meter is "middle" unit for kilometer and milimeter.

$\frac{507}{300 000} \times 244 000 000 = 412 360 m^3$

Now just convert to gallons.

$$412 360 m^3 \approx 108933987 \text{ gallons}$$