A boat takes 4 hours to cover 'D' km upstream and takes 3 hours to cover 'D - 2' km downstream. If the speed of the stream is 2 km/hr then find the distance covered by the boat in upstream in 3 hours.
This questions was previously asked in
RRB PO Prelims (05 Aug, 2023 Shift 2)
Explanation:
- The boat takes 4 hours to cover distance D km upstream.
- The boat takes 3 hours to cover distance D - 2 km downstream.
- The speed of the stream is 2 km/hr.
Let's calculate:
- Upstream speed = boat speed - stream speed.
- Downstream speed = boat speed + stream speed.
From the upstream trip:
\[ D = (boat\_speed - 2) \times 4 \]
From the downstream trip:
\[ D - 2 = (boat\_speed + 2) \times 3 \]
Solve these two equations to find the boat's speed, then determine the distance covered upstream in 3 hours:
- Let x be the boat speed.
- Equation 1: \( D = (x - 2) \times 4 \) (1)
- Equation 2: \( D - 2 = (x + 2) \times 3 \) (2)
From equation 1:
\[ x - 2 = \frac{D}{4} \]
So, \( D = 4(x - 2) \).
Substituting D from equation 1 in equation 2:
\[ 4(x - 2) - 2 = 3(x + 2) \]
Expand and solve:
\[ 4x - 8 - 2 = 3x + 6 \]
\[ 4x - 10 = 3x + 6 \]
\[ x = 16 \]
Speed of the boat = 16 km/hr.
Now, upstream speed = 16 - 2 = 14 km/hr.
Distance covered upstream in 3 hours:
\[ 3 \times 14 = 42 \]
So, the correct option is: Option 1 - 42 km
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By: Parvesh Mehta ProfileResourcesReport error