Question

unit conversions v
imperial measurements\tmetric measurements\timperial to metric
1 ft = 12 in\t10 mm = 1 cm\t1 in = 2.54 cm
3 ft = 1 yd\t100 cm = 1 m\t1 mi = 1.6 km
5,280 ft = 1 mi\t1000 m = 1 km

1. convert the following speeds to miles per hour (miles/hour)

a) 5 miles/second
b) 15840 feet/hour
c) 275 feet/minute
d) 800,000 inches/hour
e).09 miles/second
f) 777 feet/minute
g) 325 inches/second
h) 25,000 mm/second
i) 6600 yards/minute
round all answers to two decimal places

Explanation:

Step1: Recall conversion factors

1 mile = 5280 feet, 1 mile = 63360 inches, 1 hour = 3600 seconds, 1 hour = 60 minutes

Step2: Convert a) 5 miles/second to miles/hour

Multiply by 3600 (seconds in an hour). $5\times3600 = 18000$ miles/hour

Step3: Convert b) 15840 feet/hour to miles/hour

Divide by 5280 (feet in a mile). $\frac{15840}{5280}=3$ miles/hour

Step4: Convert c) 275 feet/minute to miles/hour

First convert feet to miles (divide by 5280) and minutes to hours (multiply by 60). $\frac{275}{5280}\times60=\frac{275\times60}{5280}=\frac{16500}{5280}\approx3.125\approx3.13$ miles/hour

Step5: Convert d) 800000 inches/hour to miles/hour

Divide by 63360 (inches in a mile). $\frac{800000}{63360}\approx12.63$ miles/hour

Step6: Convert e).09 miles/second to miles/hour

Multiply by 3600 (seconds in an hour). $.09\times3600 = 324$ miles/hour

Step7: Convert f) 777 feet/minute to miles/hour

First convert feet to miles (divide by 5280) and minutes to hours (multiply by 60). $\frac{777}{5280}\times60=\frac{777\times60}{5280}=\frac{46620}{5280}\approx8.83$ miles/hour

Step8: Convert g) 325 inches/second to miles/hour

First convert inches to miles (divide by 63360) and seconds to hours (multiply by 3600). $\frac{325}{63360}\times3600=\frac{325\times3600}{63360}=\frac{1170000}{63360}\approx18.47$ miles/hour

Step9: Convert h) 25000 mm/second to miles/hour

First convert mm to cm (divide by 10), cm to m (divide by 100), m to km (divide by 1000), km to miles (divide by 1.6) and seconds to hours (multiply by 3600).
$25000\ mm=\frac{25000}{10}cm = 2500\ cm=\frac{2500}{100}m=25\ m=\frac{25}{1000}km = 0.025\ km=\frac{0.025}{1.6}miles$
$\frac{0.025}{1.6}\times3600=\frac{0.025\times3600}{1.6}=\frac{90}{1.6}\approx56.25$ miles/hour

Step10: Convert i) 6600 yards/minute to miles/hour

First convert yards to feet (multiply by 3), feet to miles (divide by 5280) and minutes to hours (multiply by 60).
$6600\ yards = 6600\times3 = 19800\ feet$
$\frac{19800}{5280}\times60=\frac{19800\times60}{5280}=\frac{1188000}{5280}=225$ miles/hour

Answer:

a) 18000 miles/hour
b) 3 miles/hour
c) 3.13 miles/hour
d) 12.63 miles/hour
e) 324 miles/hour
f) 8.83 miles/hour
g) 18.47 miles/hour
h) 56.25 miles/hour
i) 225 miles/hour