Question

Help me to solve this. ​

Answer 1

Given :

• If the train would have been 10 kilometre per hour faster, it would have taken 2 hours less than the scheduled time.

• If the train were slower by 10 km per hour, it would have taken 3 hours more than the scheduled time.

To Find :

• Distance covered by the train.

Solution :

• It is stated that a train covered a certain distance at a uniform speed. If the speed of the train would have been 15 km/h more, it would have taken 1.6 hours less than the scheduled time. If the speed of the train would have been 12 km/h less, it would have taken 2 hours more than the scheduled time. So, here it has asked to find the distance covered by the train.

• So ,first we need to find out the speed and time taken by the train. Thereafter, the distance covered.

For that,

• Let us we consider the speed of the train be " x km/hr "

• Time taken by the train be " ‘y’ hrs "

So,

Let's solve it !

We know :

$\bullet \: \: { \underline{\boxed{\bf{Distance = Speed \times Time}}}}$

That is Distance covered by the train is :-

$\bullet \: \: { \underline{\boxed{\bf{ x \times y = xy}}}}$

Now, According to the question :

Case I

If the train would have been 15 km/hr more, then it would have taken 1.6 hours less than the scheduled time.

Making Equation :

$:\implies\:\:\sf (x + 15) (y - 1.6) = xy$

$:\implies\:\:\sf xy - 1.6x + 15y - 24.0 = xy$

$:\implies\:\:\sf 15y - 1.6x = 24$..(1)

Case II

• If the speed of the train would have been 12 km/h less, it would have taken 2 hours more than the scheduled time.

$: \implies \sf (x - 12) ( y + 2) = xy$

$:\implies\:\:\sf xy + 2x - 12y - 24 = xy$

$:\implies\:\:\sf - 12y + 2x = 24$..(2)

Taking (1) and (2)

Using Elimination Method by equating Coefficient

Multiplying eq (1) by (4)

So, we get ;;

$:\implies\:\:\sf 15y - 1.6x = 24 \: \: \times (4)$

$:\implies\:\:\sf 60y - 6.4x = 96$..(3)

Similarly, Multiplying eq (2) by (5)

$:\implies\:\:\sf - 12y + 2x = 24$ ..(2) × 5

$:\implies\:\:\sf - 60y + 10x = 120$ ..(4)

Now, Taking (3) and (4)

By Eliminating y from the equation , making it linear equation.

60y - 6.4x = 96 ..(3)

- 60y + 10x = 120 ..(4)

_______________ By Addition :

$:\implies\:\:\sf 3.6x = 216$

$:\implies\:\:\sf x = \dfrac{216}{3.6}$

$:\implies\:\:\sf x = \dfrac{\cancel{2160}^{\: \: 60}}{\cancel{36}^{\: \: 1}}$

$:\implies\:\:\sf x = {\red{60}}$

Therefore, The speed of the train is 60 km/hr.

Substituting the value of x in equation (4)

$:\implies\:\:\sf - 60y + 10(60) = 120$

$:\implies\:\:\sf - 60y + 600 = 120$

$:\implies\:\:\sf - 60y = 120 - 600$

$:\implies\:\:\sf - 60 y = - 480$

Negative Sign cancel out ::

$:\implies\:\:\sf y = \dfrac{\not{480}^{ \: \: \: 8} }{\not{60}^{ \: \: 1} }$

$:\implies\:\:\sf y = {\red{ 8}}$

Hence, The time taken by the train is 8 hours.

Now, we know distance is :-

$\::\implies\:\sf xy = 60 \times 8$

$:\implies\:\: \underline{ \boxed{\sf Distance = {\purple{480 \: km/hr}} }}$