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Q.

Points A and B are 70 km apart on a highway. A car starts from A and another car 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 one hour. Find the speed of the two cars.


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a

50 km/h and 30 km/h

b

40 km/h and 30 km/h

c

20 km/h and 40 km/h

d

40 km/h and 80 km/h  

answer is B.

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Detailed Solution

Given that a car starts from A and another car 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 one hour.
Also given A and B are 70km apart.
The relative speed of any two things with speeds x km/h and y km/h in
same direction = x−y km/h ,
opposite direction = x+y km/h .
We know that Distance = Speed × Time.
Let us assume speeds of the car as x km/h and y km/h.
So, the relative speed in same direction = x−y km/h …………….(1)
And, the relative speed in opposite direction = x+y km/h …………..(2)
Given that, time take to meet both the cars hour = 7 hour and
the distance between the points = 70 km.
Distance = Speed × Time
Substitute the value of speed from equation (1) in above formula, and we have time equal to 7 hour and distance 70 km.
⇒7 x−y =70 ⇒x−y= 70 10 ⇒x−y=10 ……………….(3)
Given that, time take to meet both the cars hour = 1 hour and
the distance between the points = 70 km.
Distance = Speed × Time
Substitute the value of speed from equation (2) in above formula, and we have time equal to 1 hour and distance 70 km.
⇒1 x+y =70 ⇒x+y=70 ……………..(4)
Add equation (3) and (4).
⇒x−y+x+y=10+70 ⇒x+x=80 ⇒2x=80 ⇒x= 80 2 ⇒x=40
Put in equation (4).
⇒40+y=70 ⇒y=70−40 ⇒y=30 Thus, the speed of the cars is 40 km/h and 30 km/h .
The correct option is (2).
 
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