A boat tales 1.6 hours longer to go 36 tms up a river than down the river if the speed of the water current is 4 km per hour. what is the speed of the boat in still water
Answers
Step-by-step explanation:
Answer:
The speed of the boat in still water is 14 km/hr.
Step-by-step explanation:
Given : A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hour.
To find : What is the speed of the boat in still water?
Solution :
Let the speed of the boat is x km/hr.
The speed of the river is 4 km/hr.
The upstream speed is (x-4) km/hr and downstream speed is (x+4) km/hr
We know,
speed =distance
It takes 1.6 hours longer to go 36 kms up a river than down the river.
According to question,
\frac{36}{x-4}-\frac{36}{x+4}=1.6
x−4
36
−
x+4
36
=1.6
\frac{36}{x-4}-\frac{36}{x+4}=\frac{16}{10}
x−4
36
−
x+4
36
=
10
16
\frac{9}{x-4}-\frac{9}{x+4}=\frac{2}{5}
x−4
9
−
x+4
9
=
5
2
9(x+4)-9(x-4)=\frac{2}{5}(x-4)(x+4)9(x+4)−9(x−4)=
5
2
(x−4)(x+4)
9x+36-9x+36=\frac{2}{5}(x^2-16)9x+36−9x+36=
5
2
(x
2
−16)
72=\frac{2}{5}(x^2-16)72=
5
2
(x
2
−16)
x^2-16=180x
2
−16=180
x^2=180+16x
2
=180+16
x^2=196x
2
=196
x=14x=14
Therefore, the speed of the boat in still water is 14 km/hr.