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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Answer & Solution
Correct Answer:
Option
B
Let the speed of the stream be x km/hr
Then,
Speed downstream = (15 + x) km/hr
Speed upstream = (15 - x) km/hr
$$\eqalign{ & \therefore \frac{{30}}{{ {15 + x} }} + \frac{{30}}{{ {15 - x} }} = 4\frac{1}{2} \cr & \Rightarrow \frac{{900}}{{225 - {x^2}}} = \frac{9}{2} \cr & \Rightarrow 9{x^2} = 225 \cr & \Rightarrow {x^2} = 25 \cr & \Rightarrow x = 5\,km/hr \cr} $$
Then,
Speed downstream = (15 + x) km/hr
Speed upstream = (15 - x) km/hr
$$\eqalign{ & \therefore \frac{{30}}{{ {15 + x} }} + \frac{{30}}{{ {15 - x} }} = 4\frac{1}{2} \cr & \Rightarrow \frac{{900}}{{225 - {x^2}}} = \frac{9}{2} \cr & \Rightarrow 9{x^2} = 225 \cr & \Rightarrow {x^2} = 25 \cr & \Rightarrow x = 5\,km/hr \cr} $$
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Login2*30*15/(15^2 - y^2) = 9/2 (4hr30min =9/2hr)
900/(225-y^2)= 9/2
1800/9=225-y^2
200 =225- y^2
y^2 = 25
y = 5km/h