Name: Fractions Using Cross Multiplication
Uploaded: 2019-07-19
Duration: 3 min 47 s
Description: Learn how to compare two fractions with each other by using the fairly straightforward method of cross-multiplication. Master this concept now by watching th...

Question

Two stations

A

and

B

on a highway are

90 km

apart. A car starts from

A

and another car starts from

B

at the same time. If they travel in the same direction they meet in

9

hours, but if they travel towards each other they meet in

1

hour after start. Find the speeds of the two cars, the car from

A

moving faster.

Accepted Answer

Let speed of the car moving from $A$ be $x km / h$ and that moving from $B$ be $y km / h$ .

Given that when they travel towards each other they meet in $1$ hour after the start. So, in $1$ hour, the car from $A$ will travel $= x km / h \times 1 h = x km$ . [Distance travelled $=$ speed $\times$ time]

And, in $1$ hour, the car from $B$ will travel $= y km / h \times 1 h = y km$ . [Distance travelled $=$ speed $\times$ time]

So, by the condition given in the question, we get, $x + y = 90 \Rightarrow y = 90 - x$ -----(i)

Again, given that the car from $A$ moving faster and if they travel in the same direction they meet in $9$ hours. In this case, the two cars will meet only when the car from $A$ moves towards $B$ and the car from $B$ moves away from $A$ . Hence, in $9$ hours, the car $A$ will travel $90 km +$ the distance travelled by the car $B$ .

In $9$ hours, the distance travelled by the car from $A$ $= x km / h \times 9 h = 9 x km$ . [Distance travelled $=$ speed $\times$ time]

And, in $9$ hour, the distance travelled by the car from $B$ $= y km / h \times 9 h = 9 y km$ . [Distance travelled $=$ speed $\times$ time]

So, by the condition given in the question, we get, $9 x km = 9 y km + 90 km$

$\Rightarrow 9 x = 9 y + 90$

$\Rightarrow 9 x = 9 (90 - x) + 90$

$\Rightarrow 9 x = 810 - 9 x + 90$

$\Rightarrow 9 x + 9 x = 900$

$\Rightarrow 18 x = 900$

$\Rightarrow x = \frac{900}{18} = 50$

From (i), we get, $y = 90 - x = 90 - 50 = 40$ .

Therefore, the required speed of the car starting from $A$ is $50 km / h$ and that of the car starting from $B$ is $40 km / h$

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !