A) 32.7 km/h
B) 35 km/h
C) 40 km/h
D) 45 km/h
Correct Answer: A
Solution :
Key Idea: Average speed is defined as the ratio of total distance travelled by total time taken. Let \[{{t}_{1}},{{t}_{2}},{{t}_{3}}\] be the time taken in travelling distances \[\frac{S}{3},\frac{S}{3},\frac{S}{3}.\]Then \[{{t}_{1}}=\frac{S/3}{{{v}_{1}}}=\frac{S/3}{20},{{t}_{2}}=\frac{S/3}{{{v}_{2}}}=\frac{S/3}{40},\] \[{{t}_{3}}=\frac{S/3}{{{v}_{3}}}=\frac{S/3}{60}\] \[\therefore \] Average speed \[=\frac{S}{\frac{S/3}{20}+\frac{S/3}{40}+\frac{S/3}{60}}\] \[=\frac{3}{\frac{1}{20}+\frac{1}{40}+\frac{1}{60}}\] \[=\frac{3}{\left( \frac{6+3+2}{120} \right)}\] \[=\frac{3\times 120}{11}=32.7\,\text{km/h}\]You need to login to perform this action.
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