Two cars Start moving towards each other from A and B respectivety which are 560 km apart They meet each other after 3 hr 30 min if the ratio of the speed is 3 :2 respectively, what is the difference in the time taken by the cars to cover the distance between A and B?
Answers
Answer:
D/30=160+D/50
5D=3D+480
D=240.
Total distance is D+(160+D)
= 640Km
Two cars Start moving towards each other from A and B respectively which are 560 km apart They meet each other after 3 hr 30 min if the ratio of the speed is 3 :2 respectively.
We have to find the difference in the time taken by the cars to cover the distance between A and B.
The ratio of speed of car A and B is 3 : 2.
Let the proportionality constant is x.
∴ The speed of car A = 3x
And the speed of car B = 2x
∵ both cars are moving towards each other.
∴ relative speed = speed of car A + speed of car B = 3x + 2x = 5x
Time taken = distance between A and B/relative speed
⇒ 3 hr 30 min = 560/5x
⇒ 3 + 1/2 = 7/2 = 112/x
⇒ x = 32
The speed of car A = 3x = 3 × 32 = 96 km/h
And speed of car B = 2x = 2 × 32 = 64 km/h
Now, the difference in the time taken by the cars to cover the distance between A and B = time taken by car B - time taken by car A
= 560/64 - 560/96
= 560 [1/64 - 1/96 ]
= 35/12 hr
= 2 hr 55 min
Therefore the difference in the time taken by the cars is 2 hr 55 min.
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