A man rows a boat 28 km in 4 hours downstream and same distance upstre...
Let stream flow= u km/hr
boat speed= v km/hr
therefore
A/c to question,
downstream
u+v=28/4=7 (1)
upstream
v-u=28/7=4 (2)
solve these eqn
v+u=7
v-u=4
v=11/2
u=7-(11/2)
=3/2=1.5 km/hr
option(d) Ans
A man rows a boat 28 km in 4 hours downstream and same distance upstre...
Let's assume the speed of the boat in still water is 'b' km/hr and the speed of the stream is 'c' km/hr.
Downstream Speed:
When the boat is rowing downstream, the speed of the boat is increased by the speed of the stream. So the effective speed is (b + c) km/hr.
Given that the boat rows 28 km downstream in 4 hours, we can use the formula distance = speed × time to write the equation:
28 = (b + c) × 4
Upstream Speed:
When the boat is rowing upstream, the speed of the stream is subtracted from the speed of the boat. So the effective speed is (b - c) km/hr.
Given that the boat rows 28 km upstream in 7 hours, we can again use the formula distance = speed × time to write the equation:
28 = (b - c) × 7
Solving the Equations:
We now have two equations:
28 = (b + c) × 4 ...(1)
28 = (b - c) × 7 ...(2)
To solve these equations, we can either use the substitution method or the elimination method. In this case, let's use the elimination method:
Multiply equation (1) by 7 and equation (2) by 4 to eliminate the variables 'c':
7 × 28 = 4 × (b + c)
4 × 28 = 7 × (b - c)
Simplifying these equations gives us:
196 = 4b + 4c ...(3)
112 = 7b - 7c ...(4)
Now, add equations (3) and (4) to eliminate 'c':
196 + 112 = 4b + 4c + 7b - 7c
308 = 11b - 3c
We can rearrange equation (5) to solve for 'c':
11b - 3c = 308
3c = 11b - 308
c = (11b - 308) / 3
To find the value of 'c', we need to substitute the options given in the question and check which one satisfies the equation.
Option D: c = 1.5
Substituting c = 1.5 in equation (5) gives us:
1.5 = (11b - 308) / 3
4.5 = 11b - 308
11b = 312.5
b = 28.409
Substituting the values of 'b' and 'c' in equations (1) and (2) also satisfy the given conditions.
Therefore, the correct answer is option D) 1.5 km/hr.