Question

a car with a tire of radius 16 inches rotates at 450 revolution per minute. Find the speed of the car to the nearest kilometer per hour

Answer 1

find the circumference
multiply the circumference with the # revolutions per min and that will give you the speed in inches/min

Answer 2

okay

Answer 3

2pi16=100.53

Answer 4

@ikram002p

Answer 5

\[speed=\frac{ 450\times16\times2\pi \times 1.609344 km }{ \frac{ 1hour }{60 } }=\]

Answer 6

why do i multiply 1.609344 km???

Answer 7

well anyways i get 1213.42

Answer 8

@phi

Answer 9

this problem has two parts to it. First, you figure out that the circumference is 100.53 inches
if it spins 450 times per minute, it will go 100.53 inches * 450 turns/1 minute
= 45238.93 inches per minute
that is a speed, but they want the units to be kilometers per hour
we could use 1 inch = 2.54 cm
write that as a ratio with inches on the bottom and multiply:
\[ 45238.93 \cancel{\text{ in}} \cdot \frac{2.54 \text{ cm}}{1 \cancel{\text{ in}} }= 114,906.89 \text{ cm}\]
now use 100 cm = 1 m
multiply both sides by 1000 to get
100000 cm = 1000 m or 100000 cm = 1 km
write this as a ratio with km on top and cm below, and multiply
\[ 114,906.89 \cancel{\text{cm}} \cdot \frac{1 \text{ km}}{100000 \cancel{\text{cm}} } = 1.149 \text{ km}\]
you now have
1.149 km per minute
we now change minutes to hours using 60 min = 1 hr
make a ratio with hr on top and min on the bottom
\[ 1 \cancel{ \text{ min}} \cdot \frac{ 1 \text{ hr} }{60 \cancel{ \text{ min}}}= \frac{1 }{60} \text{ hr}\]
you now have
\[ \frac{ 1.149 \text{ km}}{\frac{1}{60} \text{ hr}} \]
multiply top and bottom by 60 to get
68.94 km/hr

round to the nearest kilometer per hour 69 km/hr