A cyclist drove one kilometre, with the wind in his back, in 3 minutes and drove the same way back, against the wind, in 4 minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive 1 km without wind ?
A. $$2\frac{1}{3}$$ min
B. $$2\frac{3}{7}$$ min
C. $$3\frac{3}{7}$$ min
D. $$3\frac{7}{12}$$ min
Answer: Option C
Solution(By Examveda Team)
Let the cyclist's speed without wind be x km/hrAnd the speed of the wind be y km/hr
Then,
$$\eqalign{ & \Rightarrow \frac{1}{{x + y}} = \frac{3}{{60}} \cr & \Rightarrow x + y = 20.....(i) \cr} $$
And
$$\eqalign{ & \Rightarrow \frac{1}{{x - y}} = \frac{4}{{60}} \cr & \Rightarrow x - y = 15.....(ii) \cr} $$
Adding (i) and (ii), we get:
2x = 35 or x = 17.5
Putting x = 17.5 in (i), we get : y = 2.5
Time taken to drive 17.5 km without wind = 1 hr
Time taken to drive 1 km without wind
$$\eqalign{ & = \left( {\frac{1}{{17.5}}} \right){\text{ hr}} \cr & {\text{ = }}\left( {\frac{1}{{17.5}} \times 60} \right){\text{ min}} \cr & {\text{ = 3}}\frac{3}{7}{\text{ min}} \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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