another unit conversion?

Question

An object is traveling at 15 meters per minute. (1 kilometer=1000 meters) (1 meter= 100 centimeters)

a) convert this rate to kilometers per hourr

b) convert this rate to centimeters per second

c) how many days will it take for the object to travel 5,000,000 kilometers. (round to the nearest day)

ugh hate mathh. help please, an explanation of how you got it would be great too, thanks

Answer 1

As long as you know the unit conversions, you can always set these up as a series of fractions making the units cancel until you get the units you want. Like this:

a) 15meter/minute * 1 kilometer/1000 meters * 60 minutes/1 hour

The meters and the minutes units cancel out, and then you just do the numbers. 15*60/1000 = .9 km/hour

b) 15 m/min * 100 cm/meter * 1min/60 seconds = 25 cm/second

c) for this one, you need it in kilometers per day first:

15 m/min * 1km/1000 m * 60 min/hr * 24 hr/day = 21.6 km/day

so 1day/21.6 km * 5,000,000 km = 231,481 days

Answer 2

15 meters per minute /(1000 meters/kilometer)*60 minutes/hour
0.9 km/hr after the units are canceled.
(it might be easier to think in terms only of multiplications as in
15 m/min * 0.001 km/m * 60 min/hr )
15 m/min * 100 cm/m / 60 sec/min = 25 cm/sec
5,000,000 km /.9 km/hr gives 16 666 666.7 hours
divide that by 24 hours/day gives 694 444.444 days.

Answer 3

Set up unit conversion: You want units to cancel as you multiply through the conversion...see below, start with 15 m/min, need to convert min to h....60min=1h, when cancelling, one one bottom must cancel with something in conversions on top and vice versa

a. Given: 15 m/min

15m/min x 60min/1h x 1km/1000m = 0.90 km/h

b. 15 m/min x 100cm/1m x 1min/60 sec = 25 cm/sec

c. travels 0.90 km in 1 h
will travel 5,000,000 in x h

set up ratio: 0.90 km / 1 h = 5, 000,000/ x h
cross multiply and solve for x = 5,555,555.556 h
need answer in days, therefore divide by 24 (24 h in 1 day)
= 231,481.5 days

hope that makes sense.

Answer 4

To convert units, multiply by a fraction whose value is one, like this:

a.
(15 m / 1 min) * (60 min / 1 hr) = (900 m / 1 hr)
(900 m / 1 hr) * (1 km / 1000 m) = (0.9 km / 1 hr)
0.9 km/hr

b.
(15 m / 1 min) * (100 cm / 1 m) = (1500 cm / 1 min)
(1500 cm / 1 min) * (1 min / 60 sec) = (25 cm / 1 sec)
25 cm/sec

c.
At a rate of 0.9 km/hr, it will take:
5,000,000 km * (1 hr / 0.9 km) = 5,555,555.56 hr
5,555,555.56 hr * (1 day / 24 hr) = about 231,481 days

Answer 5

B. make sure its converted to the second power