Question

problem
three different students tried to solve the problem.
\how many kilometers in 2500. yards?\
however, they all showed different work.
student a 2500.yds×\frac{3 ft}{1 yd}×\frac{1 mile}{5280 ft}×\frac{1.609 km}{1 mile}=
student b 2500.yds×\frac{3 ft}{1 yd}×\frac{12 in}{1 ft}×\frac{2.54 cm}{1 in}×\frac{1 km}{10^{5}cm}=
student c 2500.yds×\frac{3 ft}{1 yd}×\frac{12 in}{1 ft}×\frac{1 m}{39.37 in}×\frac{1 km}{10^{3}m}=
based on their dimensional analysis, which student or students solved the problem correctly?
(note: on the exam you will need to show work on all conversion problems with dimensional analysis.)
a. students b and c solved it correctly.
b. student a solved it correctly.
c. student a and c solved it correctly.
d. all three solved in correctly.
e. none of them solved it correctly.

Explanation:

Step1: Analyze Student A's work

Student A uses the conversion factors: 1 yard = 3 feet, 1 mile = 5280 feet, 1 mile = 1.609 km.
\[2500\ yds\times\frac{3\ ft}{1\ yd}\times\frac{1\ mile}{5280\ ft}\times\frac{1.609\ km}{1\ mile}\]
The units cancel out correctly: yards cancel with yards, feet cancel with feet, miles cancel with miles, leaving only kilometers.

Step2: Analyze Student B's work

Student B uses the conversion factors: 1 yard = 3 feet, 1 foot = 12 inches, 1 inch = 2.54 cm, 1 km = 100000 cm.
\[2500\ yds\times\frac{3\ ft}{1\ yd}\times\frac{12\ in}{1\ ft}\times\frac{2.54\ cm}{1\ in}\times\frac{1\ km}{10^{5}\ cm}\]
The units cancel out correctly: yards cancel with yards, feet cancel with feet, inches cancel with inches, centimeters cancel with centimeters, leaving only kilometers.

Step3: Analyze Student C's work

Student C uses the conversion factors: 1 yard = 3 feet, 1 foot = 12 inches, 1 inch = 39.37 m (this is incorrect, 1 inch = 0.0254 m), 1 km = 1000 m.
\[2500\ yds\times\frac{3\ ft}{1\ yd}\times\frac{12\ in}{1\ ft}\times\frac{1\ m}{39.37\ in}\times\frac{1\ km}{10^{3}\ m}\]
Since the conversion factor for inches - to - meters is wrong, Student C's work is incorrect.

Answer:

B. Student A solved it correctly.
A. Students B and C solved it correctly. (Incorrect as C is wrong)
C. Student A and C solved it correctly. (Incorrect as C is wrong)
D. All three solved it correctly. (Incorrect as C is wrong)
E. None of them solved it correctly. (Incorrect as A and B are correct)
So the answer is that only Student A and Student B solved it correctly, but among the given options, the closest correct one is B. Student A solved it correctly.