A boat travels downstream and upstream for 24 km each. If the speed of boat in still water is 7 km/hr and it takes 14 hours to complete the whole jour

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A boat travels downstream and upstream for 24 km each. If the speed of boat in still water is 7 km/hr and it takes 14 hours to complete the whole journey, then what is the upstream speed?

1. 2 km/hr
2. 6 km/hr
3. 14 km/hr
4. 10 km/hr

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Correct Answer - Option 1 : 2 km/hr

Given:

Downstream distance = 24 km

Upstream distance = 24 km

Formula Used:

Speed = Distance/Time

D = B + S

U = B - S

where, D → Downstream speed, U → Upstream speed, B → Speed of the boat in still water, S → Speed of the stream.

Calculations:

24/D + 24/U = 14

⇒ 24/(B + S) + 24/(B - S) = 14

⇒ 24/(7 + S) + 24/(7 - S) = 14

⇒ [24 × (7 - S) + 24 × (7 + S)]/(7 + S) × (7 - S) = 14

⇒ 24 × 7 × 2/(49 - S2) = 14

⇒ 24 = 49 - S2

⇒ S2 = 49 - 24 = 25

⇒ S = 5 km/hr

U = (B - S)

⇒ U = (7 - 5)

⇒ U = 2 km/hr

∴ The upstream speed is 2 km/hr.