# Ex.3.7 Q3 Pair of Linear Equations in Two Variables Solution - NCERT Maths Class 10

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## Question

A train covered a certain distance at a uniform speed. If the train would have been $$10\,\rm{ km/h}$$ faster, it would have taken $$2$$ hours less than the scheduled time. And if the train were slower by $$10\,\rm{ km/h;}$$ it would have taken $$3$$ hours more than the scheduled time. Find the distance covered by the train.

Video Solution
Pair Of Linear Equations In Two Variables
Ex 3.7 | Question 3

## Text Solution

What is Known?

Changes in speed of the train as well in the time.

What is Unknown?

Distance covered by the train.

Reasoning:

Assuming uniform speed of the train be $$x\,{\rm{km/h }}$$ and time taken to travel a given distance be $$t$$ hours. Then distance can be calculated by;

${\text{Distance}} = {\rm{ Speed }} \times {\rm{ Time}}$

Steps:

Let the uniform speed of the train be $$x\,{\rm{ km/h}}$$ and the scheduled time to travel the given distance be $$t$$ hours

Then the distance be $$xt\,{\rm{ km}}$$

When the train would have been $$10\,{\rm{ km/h}}$$ faster, it would have taken $$2$$ hours less than the scheduled time;

\begin{align}\left( {x + 10} \right)\left( {t - 2} \right)& = xt\\xt - 2x + 10t - 20 &= xt\\ - 2x + 10t &= 20 \qquad \quad \left( 1 \right)\end{align}

When the train were slower by $$10\,{\rm{ km/h,}}$$ it would have taken $$2$$ hours\] more than the scheduled time;

\begin{align}\left( {x - 10} \right)\left( {t + 3} \right) &= xt\\xt + 3x - 10t - 30 &= xt\\3x - 10t &= 30 \qquad \quad \left( 2 \right)\end{align}

Adding equations $$(1)$$ and $$(2),$$ we obtain

$x = 50$

Substituting $$x = 50$$ in equation $$(1),$$ we obtain

\begin{align} - 2 \times 50 + 10t &= 20\\- 100 + 10t &= 20\\10t &= 120\\t &= \frac{{120}}{{10}}\\t &= 12 \end{align}

Therefore, distance,

$$xt = 50 \times 12 = 600$$

Hence, the distance covered by the train is $$600 \,\rm{km.}$$

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