# Given the problem below, show how to convert the metric units to standard English (or Empirical) units.How much time would it take for an airplane to reach its destination if it traveled at an...

Given the problem below, show how to convert the metric units to standard English (or Empirical) units.

How much time would it take for an airplane to reach its destination if it traveled at an average speed of 790 kilometers/hour for a distance of 4,700 kilometers?

T(time)=d(distance)/s(speed)= 4,700km/790km/hr= 5.94 hrs

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### 1 Answer

To convert the quantities as expressed in the given problem to standard English units of miles/hour and miles one should consider using conversion factors. A conversion factor is a fraction which is set up in such a was as to cancel units we wish to eliminate and leave the desired units. To obtain a conversion factor, we start with basic definitions which relate the units of measure in question:

1.00 miles = 1.6092 km

In the stated problem we wish to eliminate the km and change them to miles. Therefore our conversion factor must be set up so the miles are in the numerator and the km are in the denominator. We do this by dividing both sides of the definition by 1.6092 km:

1.00 mile/1.6092 km = 1.6092 km/1.6092km gives us the conversion factor

1 = 1.00 mile/1.6092 km

We can now use the conversion factor 1.00 mile/1.602 km to convert our given quantities.

4,700 km X (1.00 mile/1.6092km) = 2,920 miles

790 km/hr X (1.00 mile/1.6092 km) = 490 miles/hr

We can see that the time of the trip is still

T = 2,920 miles / (490 miles/hr) = 5.94 hours