Respuesta :
Answer: the speed of the stream is 6 km/h
Step-by-step explanation:
Let x represent the speed of the stream.
The speed of the motor boat in still water is 18km/h. The boat takes 1 hour more to go 24 km upstream than downstream to the same spot. This means that while going upstream, the boat moved against the direction of the stream. The total speed of the boat would be
(18 - x) and while going downstream, the boat moved in the direction of the stream. The total speed of the boat would be
(18 + x).
Time = distance/speed
The time that it took the boat to go upstream is
24/(18 - x)
Time spent upstream = time spent downstream + 1
The time that it took the boat to go downstream is
24/(18 + x) + 1
Therefore,
24/(18 - x) = 24/(18 + x) + 1
Multiplying through by 18 - x and 18 + x, it becomes
24(18 + x) = 24(18 - x) + (18 + x)(18 - x)
432 + 24x = 432 - 24x + 324 - 18x + 18x - x²
x² + 432 - 432 + 24x + 24x - 324 = 0
x² + 48x - 324 = 0
x² + 54x - 6x - 324 = 0
x( x + 54) - 6(x + 54) = 0
x - 6 = 0 or x + 54 = 0
x = 6 or x = - 54
Since the speed cannot be negative, then x = 6km/h
Answer:
Speed of the stream = 6 km/hr .
Step-by-step explanation:
We are given that speed of motorboat in still water = 18 km/hr
Let the speed of the stream = x km/hr
Now, speed of motorboat going upstream = Speed of motorboat in still
water - Speed of the stream
= (18 - x) km/hr
Speed of motorboat going downstream = Speed of motorboat in still water
+ Speed of the stream
= (18 + x) km/hr
Time taken by motorboat going upstream = [tex]\frac{Distance_u_p_s_t_r_e_a_m}{Speed of motorboat_u_p_s_t_r_e_a_m}[/tex]
= [tex]\frac{24}{(18 - x)}[/tex] hr
Time taken by motorboat going downstream = [tex]\frac{Distance_d_o_w_n_s_t_r_e_a_m}{Speed of motorboat_d_o_w_n_s_t_r_e_a_m}[/tex]
= [tex]\frac{24}{(18 + x)}[/tex] hr
Since we are given that Motorboat going upstream takes 1 hour more to go 24 km than downstream to the same spot i.e.;
Time taken by motorboat going upstream = Time taken by motorboat going downstream + 1
[tex]\frac{24}{(18 - x)}[/tex] = [tex]\frac{24}{(18 + x)}[/tex] + 1
[tex]\frac{24}{(18 - x)}[/tex] - [tex]\frac{24}{(18 + x)}[/tex] = 1
[tex]\frac{24(18+x) - 24(18-x)}{(18-x)(18+x)}[/tex] = 1
[tex]\frac{24(18+x - 18+x)}{(18-x)(18+x)}[/tex] = 1
[tex]\frac{24(2x)}{(18-x)(18+x)}[/tex] = 1
[tex]\frac{48x}{18^{2} -x^{2} }[/tex] = 1
48*x = [tex]18^{2} -x^{2}[/tex]
[tex]x^{2} +48x -324 = 0[/tex]
Now, using middle term splitting method to solve above equation;
[tex]x^{2} +54x-6x-324 = 0[/tex]
x(x + 54) - 6(x + 54) = 0
(x - 6) * (x + 54) = 0
So, either (x - 6) = 0 or (x + 54) = 0 i.e. either x = 6 or x = -54
Since x is the speed of stream and speed can't be negative so, the speed of stream = 6 km/hr.
