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

Speed of boat in still water = 40 mph

Rate of current = 10 mph

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 =
`(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 =
`(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 = (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