A train travels $360km$at uniform speed. If the speed had been $5km/hr$more, it would have taken $1hr$ less for the same journey. Find the speed of the train.
Last updated date: 23rd Mar 2023
•
Total views: 310.2k
•
Views today: 5.87k
Answer
310.2k+ 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
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
