Answer
Verified
482.7k+ views
Hint: - Use, ${\text{Speed}} = \dfrac{{{\text{Distance}}}}{{{\text{time}}}}$
Let the speed of the train be $x{\text{ }}km/hr$.
And the time to cover $360km $be $t{\text{ }} hr$.
As you know,${\text{Speed}} = \dfrac{{{\text{Distance}}}}{{{\text{time}}}}$
$\therefore x = \dfrac{{360}}{t}km/hr............\left( 1 \right)$
It is also given that if speed is increased by $5km/hr$, the time to cover $360km $is $1hr$ less than the previous time.
$\therefore x + 5 = \dfrac{{360}}{{t - 1}}km/hr.............\left( 2 \right)$
From equation (1) and (2)
$
xt = \left( {x + 5} \right)\left( {t - 1} \right) \\
\therefore xt = xt - x + 5t - 5 \\
\therefore x - 5t + 5 = 0..............\left( 3 \right) \\
$
From equation (1) $t = \dfrac{{360}}{x}$
Substitute this value in equation (3)
$
x - 5\left( {\dfrac{{360}}{x}} \right) + 5 = 0 \\
{x^2} + 5x - 1800 = 0 \\
$
Now, factorize the above equation
$
{x^2} + 45x - 40x - 1800 = 0 \\
x\left( {x + 45} \right) - 40\left( {x + 45} \right) = 0 \\
\left( {x + 45} \right)\left( {x - 40} \right) = 0 \\
\left( {x + 45} \right) = 0,{\text{ }}\left( {x - 40} \right) = 0 \\
\therefore x = - 45,{\text{ }}x = 40 \\
$
Speed cannot be negative
So the required speed is $40{\text{ }}km/hr$
Note: -In such types of questions the key concept we have to remember is that always remember the formula of speed, time, and distance, then formulate the equations using this formula and the given conditions, then simplify the equations using substitution, then we will get the required answer.
Let the speed of the train be $x{\text{ }}km/hr$.
And the time to cover $360km $be $t{\text{ }} hr$.
As you know,${\text{Speed}} = \dfrac{{{\text{Distance}}}}{{{\text{time}}}}$
$\therefore x = \dfrac{{360}}{t}km/hr............\left( 1 \right)$
It is also given that if speed is increased by $5km/hr$, the time to cover $360km $is $1hr$ less than the previous time.
$\therefore x + 5 = \dfrac{{360}}{{t - 1}}km/hr.............\left( 2 \right)$
From equation (1) and (2)
$
xt = \left( {x + 5} \right)\left( {t - 1} \right) \\
\therefore xt = xt - x + 5t - 5 \\
\therefore x - 5t + 5 = 0..............\left( 3 \right) \\
$
From equation (1) $t = \dfrac{{360}}{x}$
Substitute this value in equation (3)
$
x - 5\left( {\dfrac{{360}}{x}} \right) + 5 = 0 \\
{x^2} + 5x - 1800 = 0 \\
$
Now, factorize the above equation
$
{x^2} + 45x - 40x - 1800 = 0 \\
x\left( {x + 45} \right) - 40\left( {x + 45} \right) = 0 \\
\left( {x + 45} \right)\left( {x - 40} \right) = 0 \\
\left( {x + 45} \right) = 0,{\text{ }}\left( {x - 40} \right) = 0 \\
\therefore x = - 45,{\text{ }}x = 40 \\
$
Speed cannot be negative
So the required speed is $40{\text{ }}km/hr$
Note: -In such types of questions the key concept we have to remember is that always remember the formula of speed, time, and distance, then formulate the equations using this formula and the given conditions, then simplify the equations using substitution, then we will get the required answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE