A bicyclist is traveling at 6.7 meters per second. Which of the mathematical operation would correctly determine the speed in miles per hour? A . 6 .7 m s × 1000 km 1 m × 0.621 mi 1 km × 60 s 1 min × 60 min 1 hr B . 6 .7 m s × 1 km 1000 m × 1 km 0.621 mi × 60 s 1 min × 60 min 1 hr C . 6 .7 m s × 1 km 1000 m × 0.621 mi 1 km × 60 s 1 min × 60 min 1 hr D . 6.7 m s × 1 km 1000 m × 0.621 mi 1 km × 1 min 60 s × 1 hr 60 min E . 6 .7m s × 1000 m 1 km × 0 .621 mi 1 km × 1 min 60 s × 1 hr 60 min Explain what is wrong with the incorrect responses.
A bicyclist is traveling at 6.7 meters per second. Which of the mathematical operation would correctly determine the speed in miles per hour? A . 6 .7 m s × 1000 km 1 m × 0.621 mi 1 km × 60 s 1 min × 60 min 1 hr B . 6 .7 m s × 1 km 1000 m × 1 km 0.621 mi × 60 s 1 min × 60 min 1 hr C . 6 .7 m s × 1 km 1000 m × 0.621 mi 1 km × 60 s 1 min × 60 min 1 hr D . 6.7 m s × 1 km 1000 m × 0.621 mi 1 km × 1 min 60 s × 1 hr 60 min E . 6 .7m s × 1000 m 1 km × 0 .621 mi 1 km × 1 min 60 s × 1 hr 60 min Explain what is wrong with the incorrect responses.
A bicyclist is traveling at 6.7 meters per second. Which of the mathematical operation would correctly determine the speed in miles per hour?
A
.
6
.7
m
s
×
1000
km
1
m
×
0.621
mi
1
km
×
60
s
1
min
×
60
min
1
hr
B
.
6
.7
m
s
×
1
km
1000
m
×
1
km
0.621
mi
×
60
s
1
min
×
60
min
1
hr
C
.
6
.7
m
s
×
1
km
1000
m
×
0.621
mi
1
km
×
60
s
1
min
×
60
min
1
hr
D
.
6.7
m
s
×
1
km
1000
m
×
0.621
mi
1
km
×
1
min
60
s
×
1
hr
60
min
E
.
6
.7m
s
×
1000
m
1
km
×
0
.621
mi
1
km
×
1
min
60
s
×
1
hr
60
min
Explain what is wrong with the incorrect responses.
(A)
Expert Solution
Interpretation Introduction
Interpretation:
Whether the given mathematical operation gives the value of speed in miles per hour is correct or not is to be determined.
Explanation of Solution
The distance traveled by an object per unit time is known as speed. The SI unit of speed is meter per second m/s . It can also be measured in centimeters per second cm/s , kilometer per hour km/h , and miles per hour mi/h .
The conversion factor from m to km is expressed as follows:
1 m=0.001 km1=1 km1000 m
The conversion factor from m/s to mi/h is expressed as follows:
1 m/s=2.236 mi/hr1=2.236 mi/hr1 m/s
In the given mathematical operation 6.7 ms×1000 km1 m×0.621mi1 km×60 s1 min×60 min1 hr , the conversion factor for meters to kilometers is incorrect. It should be 1 km1000 m . Therefore, the mathematical operation 6.7 ms×1 km1000 m×0.621mi1 km×60 s1 min×60 min1 hr gives the correct values of speed in mi/h .
(B)
Expert Solution
Interpretation Introduction
Interpretation:
Whether the given mathematical operation gives the value of speed in miles per hour is correct or not is to be determined.
Explanation of Solution
The conversion factor from km to miles is expressed as follows:
1 km=0.621 miles1=0.621 miles1 km
In the given mathematical operation 6.7 ms×1000 km1 m×1 km0.621 mi×60 s1 min×60 min1 hr , the conversion factor for kilometers to miles is incorrect. It should be 0.621miles1 km . Therefore, the correct mathematical operation 6.7 ms×1 km1000 m×0.621mi1 km×60 s1 min×60 min1 hr gives the values of speed in mi/h .
(C)
Expert Solution
Interpretation Introduction
Interpretation:
Whether the given mathematical operation gives the value of speed in miles per hour is correct or not is to be determined.
Explanation of Solution
The given mathematical operation 6.7 ms×1 km1000 m×0.621 mi1 km×60 s1 min×60 min1 hr is appropriate to find the speed in miles per hour.
(D)
Expert Solution
Interpretation Introduction
Interpretation:
Whether the given mathematical operation gives the value of speed in miles per hour is correct or not is to be determined.
Explanation of Solution
The conversion factor from minute to second is expressed as follows:
1 min=60 s1=60 s1 min
The conversion factor from hr to min is expressed as follows:
1 hr=60 min1=60 min1 hr
In the given mathematical operation 6.7 ms×1 km1000 m×0.621 mi1 km×1 min60 s×1 hr60min , the conversion factors in the fourth and fifth steps are incorrect. It should be 60 s1 min and 60 min1 hr , respectively.
Therefore, the correct mathematical operation 6.7 ms×1 km1000 m×0.621mi1 km×60 s1 min×60 min1 hr gives the values of speed in mi/h .
(E)
Expert Solution
Interpretation Introduction
Interpretation:
Whether the given mathematical operation gives the value of speed in miles per hour is correct or not is to be determined.
Explanation of Solution
The conversion factor from hr to min is expressed as follows:
1 hr=60 min1=60 min1 hr
The conversion factor from m to km is expressed as follows:
1 m=0.001 km1=1 km1000 m
The conversion factor from minute to second is expressed as follows:
1 min=60 s1=60 s1 min
In the given mathematical operation 6.7 ms×1000 m1 km×0.621 mi1 km×1 min60 s×1 hr60min , the conversion factors in the second and last two steps are incorrect. It should be 1 km1000 m , 60 s1 min , and 60 min1 hr , respectively.
Therefore, the correct mathematical operation 6.7 ms×1 km1000 m×0.621mi1 km×60 s1 min×60 min1 hr gives the values of speed in mi/h .
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