Name: Cross Multiplication Method: Illustration
Uploaded: 2019-07-19
Duration: 7 min 27 s
Description: This tutorial will show you many examples of solving linear equations in two variables using the cross-multiplication method with a clear step-by-step explan...

Question

A man walks a certain distance with certain speed. If he walks

1 / 2 km

an hour faster, he takes

1

hour less. But, if he walks

1 km

an hour slower, he takes

3

more hours. Find the distance covered by the man and his original rate of walking.

Accepted Answer

Let the actual speed of the train be $x km / hr$ and the actual time taken is $y$ hours.
Then,
Distance covered $= Speed \times Time$ $= x \times y$ $= x y$
If the speed is increased by $\frac{1}{2} km / hr$ , then time of journey is reduced by $1$ hour i.e., when speed is $(x + \frac{1}{2}) km / hr$ , time of journey is $(y - 1) hours$ .
$\Rightarrow x y = (x + \frac{1}{2}) (y - 1)$
$\Rightarrow x y = x y + \frac{y}{2} - x - \frac{1}{2}$
$\Rightarrow 0 = \frac{y - 2 x - 1}{2}$
$\Rightarrow - 2 x + y = 1$ ...(i)

When the speed is reduced by $1$ $km / hr$ , then the time of journey is increased by $1$ hours i.e., when speed is $1 km$ , time of journey is $(y + 3) hrs$ .
$x y = (x - 1) (y + 3)$
$x y = x y - 1 y + 3 x - 3$
$x y - x y = 3 x - 1 y - 3$
$3 x - 1 y = 3 \dots (i i)$

By using elimination method on equation (ii) and (i), we have:
$x = 4$
Putting the value $x = 4$ in equation (ii), we get:
$3 x - 1 y - 3 = 0$
$3$ x $4 - 1 y - 3 = 0$
$12 - 1 y - 3 = 0$
$12 - 3 - 1 y = 0$
$9 - 1 y = 0$
$- 1 y = - 9$
$1 y = 9$
$y = 9$
Hence, the speed of train is $4 \times 9 = 36$ $km$ and original speed is $4 km / hr$ .

A man walks a certain distance with certain speed. If he walks $1 / 2 km$ an hour faster, he takes $1$ hour less. But, if he walks $1 km$ an hour slower, he takes $3$ more hours. Find the distance covered by the man and his original rate of walking.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

A man walks a certain distance with certain speed. If he walks $1 / 2 km$ an hour faster, he takes $1$ hour less. But, if he walks $1 km$ an hour slower, he takes $3$ more hours. Find the distance covered by the man and his original rate of walking.