A boat takes 90 minutes less to travel 36 km downstream than to travel

1.	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
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.

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

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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