Question

Points A and B are $70km$ apart on a highway. A car starts from A and another starts from B simultaneously. If they travel in the same direction, they meet in 7 hours. But, if they travel towards each other, they meet in 1 hour. Find the speed of each car in km/hr.​

• A. 30 and 20
• B. 40 and 30
• C. 40 and 45
• D. 30 and 25

Answer 1

The correct option is B 40 and 30

Let P and Q be the cars starting from A and B respectively and let their speeds be x km/hr and y km/hr respectively.​
Case- I​
When the cars P and Q move in the same direction.​
Distance covered by the car P in 7 hours $=7xkm$​
Distance covered by the car Q in 7 hours $=7ykm$​
Let the cars meet at point M.

AM= 7x and BM=7y
AM-BM=AB
$7x-7y=70$
$\Rightarrow x-y=10$
Case II​
When the cars P and Q move in opposite directions. ​
Distance covered by P in 1 hour $=xkm$​
Distance covered by Q in 1 hour $=ykm$​
​
In this case let the cars meet at a point N.​

AN= x km and BN= y km
$x+y=70$
Adding (1) and (2), we get​
$2x=80$ ​
$\Rightarrow x=40$
​
Putting $x=40$ in (1), we get​
$40-y=10$​
$\Rightarrow y=30$
$x=40,y=30$
Hence, the speeds of these cars are 40 km/ hr and 30 km/ hr respectively.​