Question

a motorboat takes 5 hours to travel 150 Miles going Upstream. the return trip takes 3 hours going Downstream .what is the rate of the boat in still water and what is the rate of the current ?​

Answer 1

Answer:

Speed of boat in still water = 40 mph

Rate of current = 10 mph

Step-by-step explanation:

Let the speed of boat in still water be x & let the speed of the stream be y.

Total Distance = 150 miles

Time taken to travel during upstream = 5 hrs

Speed of the boat during upstream = $\frac{150}{5} = 30\:mph$

Speed of boat during upstream can be represented as $x - y = 30$ because the boat is moving in the opposite direction of flow of stream.

Time taken to travel during downstream = 3 hrs

Speed of boat during downstream = $\frac{150}{3} = 50\:mph$

Speed of boat during downstream can be represented as $x+y=50$ because the boat is moving in the same direction of flow of stream.

We got a pair of linear eqns. Let  $x-y=30$ be eqn.1 and $x+y=50$ be eqn.2 . Using substitution method ,

From eqn.1 , $x-y=30$

$=> x = y + 30$

Putting 'x' in eqn.2 , $x + y = 50$

$=> y + 30 + y = 50$

$=> y + y = 50-30$

$=> 2y = 20$

$=> y = \frac{20}{2} = 10\: mph$

Putting y in eqn.1 ,

$x - 10 = 30$

$=> x = 30 + 10 = 40 \:mph$

Hence , the speed of boat in still water is 40 mph and speed of stream is 10 mph