A boat takes 51 minutes to go 10.2 km upstream. The ratio of the speed of the boat in still water to that of the stream is 7 : 6. How much total time (in hours) will the boat take to go 17.7 km upstream and 66.3 km downstream?

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  1. 3.4
  2. 0.3
  3. 1.9
  4. 2.1

Answer (Detailed Solution Below)

Option 3 : 1.9
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Detailed Solution

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Given:

Upstream time = 51 minutes = 51 ÷ 60 = 0.85 hours

Upstream distance = 10.2 km

Speed ratio (boat : stream) = 7 : 6

Formula used:

Speed = Distance ÷ Time

Upstream speed = Boat speed − Stream speed

Downstream speed = Boat speed + Stream speed

Calculations:

⇒ Upstream speed = 10.2 ÷ 0.85 = 12 km/hr

Let boat speed = 7x, stream speed = 6x ⇒ upstream = 7x − 6x = x

⇒ x = 12 ⇒ boat speed = 7x = 84 km/hr, stream speed = 6x = 72 km/hr

⇒ Downstream speed = 84 + 72 = 156 km/hr

⇒ Time for 17.7 km upstream = 17.7 ÷ 12 = 1.475 hours

⇒ Time for 66.3 km downstream = 66.3 ÷ 156 = 0.425 hours

⇒ Total time = 1.475 + 0.425 = 1.9 hours

∴ Total time taken = 1.9 hours

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