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in Distance, Time and Speed by (49.2k points)
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A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, the speed of the stream is 

(a) 4 km/hr 

(b) 3 km/hr 

(c) 2.5 km/hr 

(d) 2 km/hr

1 Answer

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Best answer

(d) 2 km/hr

Let the speed of the stream be x km/hr. 

Speed of boat in still water = 10 km/hr 

∴ Speed of boat downstream = (10 + x) km/hr 

Speed of boat upstream = (10 – x) km/hr

Given, \(\frac{36}{(10-x)}-\frac{36}{(10+x)}=\frac{90}{60}\)

⇒ \(\frac{36(10+x)-36(10-x)}{(10-x)(10+x)}=\frac32\)

⇒ \(\frac{72x}{100-x^2}=\frac32\) ⇒ 144x = 300 – 3x2

⇒ 3x2 + 144x – 300 = 0 

⇒ 3x2 + 150x – 6x – 300 = 0 

⇒ 3x(x + 50) –6(x + 50) = 0 

⇒ (3x – 6) (x + 50) = 0 

⇒ x = 2 or –50. 

Since speed is not negative, x = 2 km/hr.

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