Question : Points 'A' and 'B' are 70 km apart on a highway. A car starts from 'A' and another from 'B' at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars (in km/hr).
Option 1: 20, 30
Option 2: 40, 30
Option 3: 30, 50
Option 4: 20, 40
Correct Answer: 40, 30
Solution :
Let the speed of the car starting from A be $x$ km/hr and that from B be $y$ km/hr. ($x>y$)
In opposite direction, relative speed = $(x+y)$ km/hr
In same direction, relative speed = $(x-y)$ km/hr
Distance = 70 km
⇒ $\frac{70}{x-y}$ = 7 [Use: Time = $\frac{\text{Relative Distance}}{\text{Relative Speed}}$]
⇒ $x-y$ = 10 --------------(i)
Also, $\frac{70}{x+y}$ = 1 [Use: Time = $\frac{\text{Relative Distance}}{\text{Relative Speed}}$]
⇒ $x+y$ = 70 --------------(ii)
Adding (i) and (ii),
$2x$ = 80
⇒ $x$ = 40 km/hr
Subtracting (i) from (ii),
$2y$ = 60
⇒ $y$ = 30 km/hr
Hence, the correct answer is 40, 30.
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