Two cyclists, k kilometres apart, and starting at the same time, would be together in r hours if they travelled in the same direction, but would pass each other in t hours if they travelled in opposite directions. The ratio of the speed of the faster cyclist to that of the slower is :
A. $$\frac{{r + t}}{{r - t}}$$
B. $$\frac{r}{{r - t}}$$
C. $$\frac{{r + t}}{r}$$
D. $$\frac{r}{t}$$
Answer: Option A
Solution(By Examveda Team)
Let the speed of the faster and slower cyclists be x km/hr and y km/hr respectivelyThen,
$$\eqalign{ & \frac{k}{{x - y}} = r \cr & \left( {x - y} \right)r = k.....(i) \cr & {\text{And,}} \cr & \frac{k}{{x + y}} = t \cr & \left( {x + y} \right)t = k.....(ii) \cr} $$
From (i) and (ii), we have :
$$\eqalign{ & \Rightarrow \left( {x - y} \right)r = \left( {x + y} \right)t \cr & \Rightarrow xr - yr = xt + yt \cr & \Rightarrow xr - xt = yr + yt \cr & \Rightarrow x\left( {r - t} \right) = y\left( {r + t} \right) \cr & \Rightarrow \frac{x}{y} = \frac{{r + t}}{{r - t}} \cr} $$
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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