MCQ Word Problem 1 ( Boat in a stream and distance calculation )
MCQ Word Problem 1: A steamer goes downstream from one port to another in 4 hours, it covers the same distance upstream in 5 hours. If the speed of the stream is 2km/hr,the distance between the two parts is______?
a) 50 km/hr b) 60 km/hr c) 70 km/hr d) 80 km/hr
Solution:
We in this word math problem know ;
Distance = Speed x Time
So,
\[ Speed = \frac{Distance}{Time} \]
Let Distance between two ports is ‘x’
Upstream
Speed of Streamer = \( \frac{x }{5}\frac{Km}{hr} \)
Downstream
Speed of Streamer = \( \frac{x }{4}\frac{Km}{hr} \)
We know that ;
Speed of Stream = \( \frac{His Downstream Speed – His Upstream Speed}{2} \)
So,
Speed of Stream =\( \frac{x/4-x/5}{2}\frac{km}{hr} \)
But given that speed of stream is 2 km/hr;
So,
\[ 2=\frac{x/4-x/5}{2}\frac{km}{hr} \]
Simplifying we get;
\[ x=80 \]
So for this word math problem, the distance between two ports is 80 kms – option d is correct!
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