Billy Bob was driving at 115 kilometers per hour to investigate his bacteria growth culture which was growing at 54.3 milligrams per week.

Question

*Convert the driving speed to feet per second.

*Convert the growth rate to kilograms per year.

Answer 1

To solve this conversion, we need to multiply the original value,115km/hr, by a series of factors that equal one, such that the original value does not change and the units of each consecutive factor cancel until we are left with the desired unit ratio.

for example, if there are 1000m in 1km, then the ratio of 1000m/1km equals 1

and when the original value is multiplied by that ratio, the original value doesn't change, because

anything multiplied by 1 remains the same value. The unit of km, however, cancels leaving m instead.

115km x 1000m = 115,000m

1km

^{note: when deciding which way to write the multiplying factor, keep in mind that in order for km to cancel from the numerator of}

^{the given value, km must be in the denominator of the next factor to ensure they cancel, rather than multiply together}

driving speed conversion "plan":

km → m → cm → in → ft

hr → min → s

_{note: ft is four steps away from km and s is two steps away from hr, therefore we will multiply the original value by a total of six}

_{conversion factors}

_{(1) (2) (3) (4) (5) (6)}

^{set it up}

115km _x 1000m _x 100cm _x 1in _x 1ft _x 1hr _x 1min

hr 1km 1m 2.54cm 12in 60min 60s

^{cancel what can be cancelled}

115km _x 1000m _x 100cm _x 1in _x 1ft _x 1hr _x 1min = 105 ft

hr 1km 1m 2.54cm 12in 60min 60s s

^{everything that didn't cancel is the answer, now just evaluate}

bacterial growth rate conversion "plan":

mg → g → kg

wk → yr

54.3mg _x 1g _x 1kg _x 52wk = 2.82 x10^-3 kg

wk 1000mg 1000g 1yr yr

Answer 2

1) Converting 115 km per hour to feet per second

We can these unit conversions:

1. 1 kilometer = 1000 meters
2. 1 meter = 3.28084 feet
3. 1 hour = 3600 seconds

115 km/hr x 1000 m/km x 3.28084 ft/m x 1 hr/3600 s

= 104.79 ft/s

2) Converting 54.3 miligrams per week to kilograms per year

We can use these unit conversions:

1. 52 weeks = 1 year
2. 1 kilogram = 1,000,000 milligrams

54.3 mg/week x 52 weeks/year x 1 kg/1,000,000 mg

= 0.00282 kg/year