Answer
Verified
40.8k+ views
Hint: First, before proceeding for this, we need to suppose the speed of the boat in upstream be x km/hr and speed for the downstream as y km/hr. Then, the condition given in the question clearly says that the distance covered for upstream in 8 hrs 48 min is equal to the distance covered for downstream in 4 hrs. Then, now we should be aware of the formulas for the speed of the boat and speed of the water stream as $\dfrac{x+y}{2}$and $\dfrac{y-x}{2}$respectively. Then, by using the ratio calculated above, we get the ratio between the speed of the boat and the speed of the water current.
Complete step-by-step answer:
In this question, we are supposed to find the ratio between the speed of the boat and the speed of the water current respectively when a boat running upstream takes 8 hours 48 min to cover a certain distance, while it take 4 hours to cover the same distance downstream.
So, before proceeding for this, we need to suppose the speed of the boat in upstream be x km/hr and speed for the downstream as y km/hr.
Now, the condition given in the question clearly says that the distance covered for upstream in 8 hrs 48 min is equal to the distance covered for downstream in 4 hrs.
Now, by using the above condition we get the equation as multiplication of speed for downstream to its time and multiplication of upstream speed with its time as:
$x\times 8\dfrac{48}{60}=y\times 4$
Then, we will solve the above expression to get the value of the ratio x:y as:
$\begin{align}
& 8\dfrac{4}{5}x=4y \\
& \Rightarrow \dfrac{44}{5}x=4y \\
& \Rightarrow \dfrac{x}{y}=\dfrac{4\times 5}{44} \\
& \Rightarrow \dfrac{x}{y}=\dfrac{5}{11} \\
\end{align}$
So, now we should be aware of the formulas for the speed of the boat and speed of the water stream as:
Then, speed of the boat is given by $\dfrac{x+y}{2}$.
Then, speed of the water stream is given by $\dfrac{y-x}{2}$.
So, now by dividing the speed of the boat with the speed of the water current to get the ratio as:
$\dfrac{\dfrac{x+y}{2}}{\dfrac{y-x}{2}}=\dfrac{x+y}{y-x}$
Now, divide the numerator and denominator by y to get the required ratio as:
$\dfrac{\dfrac{x}{y}+1}{1-\dfrac{x}{y}}$
Then, by substituting the value of $\dfrac{x}{y}$as $\dfrac{5}{11}$ calculated above to get the ratio as:
\[\begin{align}
& \dfrac{\dfrac{5}{11}+1}{1-\dfrac{5}{11}}=\dfrac{\dfrac{5+11}{11}}{\dfrac{11-5}{11}} \\
& \Rightarrow \dfrac{16}{6} \\
& \Rightarrow \dfrac{8}{3} \\
\end{align}\]
So, we get the ratio between the speed of the boat and the speed of the water current respectively as 8:3.
Hence, option (c) is correct.
Note: Now, to solve these types of the questions we need to know some of the basic formulas for the time, speed and distance. So, we must know the relation between speed(s), time (t) and distance (d) as:
$s=\dfrac{d}{t}$
Complete step-by-step answer:
In this question, we are supposed to find the ratio between the speed of the boat and the speed of the water current respectively when a boat running upstream takes 8 hours 48 min to cover a certain distance, while it take 4 hours to cover the same distance downstream.
So, before proceeding for this, we need to suppose the speed of the boat in upstream be x km/hr and speed for the downstream as y km/hr.
Now, the condition given in the question clearly says that the distance covered for upstream in 8 hrs 48 min is equal to the distance covered for downstream in 4 hrs.
Now, by using the above condition we get the equation as multiplication of speed for downstream to its time and multiplication of upstream speed with its time as:
$x\times 8\dfrac{48}{60}=y\times 4$
Then, we will solve the above expression to get the value of the ratio x:y as:
$\begin{align}
& 8\dfrac{4}{5}x=4y \\
& \Rightarrow \dfrac{44}{5}x=4y \\
& \Rightarrow \dfrac{x}{y}=\dfrac{4\times 5}{44} \\
& \Rightarrow \dfrac{x}{y}=\dfrac{5}{11} \\
\end{align}$
So, now we should be aware of the formulas for the speed of the boat and speed of the water stream as:
Then, speed of the boat is given by $\dfrac{x+y}{2}$.
Then, speed of the water stream is given by $\dfrac{y-x}{2}$.
So, now by dividing the speed of the boat with the speed of the water current to get the ratio as:
$\dfrac{\dfrac{x+y}{2}}{\dfrac{y-x}{2}}=\dfrac{x+y}{y-x}$
Now, divide the numerator and denominator by y to get the required ratio as:
$\dfrac{\dfrac{x}{y}+1}{1-\dfrac{x}{y}}$
Then, by substituting the value of $\dfrac{x}{y}$as $\dfrac{5}{11}$ calculated above to get the ratio as:
\[\begin{align}
& \dfrac{\dfrac{5}{11}+1}{1-\dfrac{5}{11}}=\dfrac{\dfrac{5+11}{11}}{\dfrac{11-5}{11}} \\
& \Rightarrow \dfrac{16}{6} \\
& \Rightarrow \dfrac{8}{3} \\
\end{align}\]
So, we get the ratio between the speed of the boat and the speed of the water current respectively as 8:3.
Hence, option (c) is correct.
Note: Now, to solve these types of the questions we need to know some of the basic formulas for the time, speed and distance. So, we must know the relation between speed(s), time (t) and distance (d) as:
$s=\dfrac{d}{t}$
Recently Updated Pages
Let gx 1 + x x and fx left beginarray20c 1x 0 0x 0 class 12 maths JEE_Main
The number of ways in which 5 boys and 3 girls can-class-12-maths-JEE_Main
Find dfracddxleft left sin x rightlog x right A left class 12 maths JEE_Main
Distance of the point x1y1z1from the line fracx x2l class 12 maths JEE_Main
In a box containing 100 eggs 10 eggs are rotten What class 12 maths JEE_Main
dfracddxex + 3log x A ex cdot x2x + 3 B ex cdot xx class 12 maths JEE_Main
Other Pages
The rms and average value of the voltage wave shown class 12 physics JEE_Main
How many grams of concentrated nitric acid solution class 11 chemistry JEE_Main
Explain the construction and working of a GeigerMuller class 12 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
The figure below shows regular hexagons with charges class 12 physics JEE_Main
The radius of the sphere is 43 pm 01cm The percentage class 11 physics JEE_Main