Ritu can row downstream 20 kms in 2 hours and upstream 4 km in 2 hours. What is the speed of the current ?

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Ritu can row downstream 20 kms in 2 hours and upstream 4 km in 2 hours. What is the speed of the current ?

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Answer 1 · 2018-01-26T19:57:15

The speed of the current is $4 \frac{k m}{h r}$ $4 (km)/(hr)$ .

Explanation:

Let $V_{r}$ $V_r$ be Ritu's speed in still water. Let V_s# be the stream's speed. Downstream, the 2 speeds help each other.

$(V_{r} + V_{s}) \cdot 2 h r s = 20 k m$ $(V_r + V_s)*2 hrs = 20 km$

Upstream, the 2 speeds are in opposite directions.

$(V_{r} - V_{s}) \cdot 2 h r s = 4 k m$ $(V_r - V_s)*2 hrs = 4 km$

Multiply the 2 hrs through the parentheses in both expressions.
$V_{r} \cdot 2 h r s + V_{s} \cdot 2 h r s = 20 k m$ $V_r*2 hrs + V_s*2 hrs = 20 km$
$V_{r} \cdot 2 h r s - V_{s} \cdot 2 h r s = 4 k m$ $V_r*2 hrs - V_s*2 hrs = 4 km$

Solve both expressions for the $V_{r} \cdot 2 h r s$ $V_r*2 hrs$ terms and then set the 2 expressions that are equal to $V_{r} \cdot 2 h r s$ $V_r*2 hrs$ instead equal to each other.
$V_{r} \cdot 2 h r s = - V_{s} \cdot 2 h r s + 20 k m$ $V_r*2 hrs = -V_s*2 hrs + 20 km$
$V_{r} \cdot 2 h r s = V_{s} \cdot 2 h r s + 4 k m$ $V_r*2 hrs = V_s*2 hrs + 4 km$

Therefore,
$- V_{s} \cdot 2 h r s + 20 k m = V_{s} \cdot 2 h r s + 4 k m$ $-V_s*2 hrs + 20 km = V_s*2 hrs + 4 km$

Solve for $V_{s}$ $V_s$ .
$16 k m = V_{s} \cdot 2 h r s + V_{s} \cdot 2 h r s = V_{s} \cdot 4 h r s$ $16 km = V_s*2 hrs + V_s*2 hrs = V_s*4 hrs$
$V_{s} \cdot 4 h r s = 16 k m$ $V_s*4 hrs = 16 km$

$V_{s} = \frac{16 k m}{4 h r s} = 4 \frac{k m}{h r}$ $V_s = (16 km)/(4 hrs) = 4 (km)/(hr)$

Just for fun, what is Ricu's speed in still water?
$V_{r} \cdot 2 h r s + V_{s} \cdot 2 h r s = 20 k m$ $V_r*2 hrs + V_s*2 hrs = 20 km$

$V_{r} \cdot 2 h r s + 4 \frac{k m}{h r} \cdot 2 h r s = 20 k m$ $V_r*2 hrs + 4 (km)/(hr)*2 hrs = 20 km$

$V_{r} \cdot 2 h r s = 20 k m - 4 \frac{k m}{h r} \cdot 2 h r s = 20 k m - 8 k m = 12 k m$ $V_r*2 hrs = 20 km - 4 (km)/(hr)*2 hrs = 20 km - 8 km = 12 km$

$V_{r} = \frac{12 k m}{2 h r s} = 6 \frac{k m}{h r}$ $V_r = (12 km)/(2 hrs) = 6 (km)/(hr)$

I hope this helps,
Steve

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Ritu can row downstream 20 kms in 2 hours and upstream 4 km in 2 hours. What is the speed of the current ?

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