Question:
Out of 940km journey,a part of journey was covered by a motar carat a speed of 72km/h . The remaining part of the journey was covered by train at a speed of 84km/h.If the total diatance was covered in 12h,find the distance travelled by train and time taken by it to cover by it.
Answer:
Given, total distance is 980 km.
Let the distance covered by car is x km
So, the distance covered by train is (940 - x) km
Time taken to cover x km distance by car = x/72 hrs (Time = distance/speed )
Time taken to cover (940 - x) km distance by train = (940 - x)/84 hrs
Given, total time taken to cover 940 km = 12 hrs
=> x/72 + (940 - x)/84 = 12
=> {7x + 6(940 - x)}/504 = 12 {LCM(72, 84) = 504}
=> (7x + 5640 - 6x)/504 = 12
=> x + 5640 = 12 * 504
=> x + 5640 = 6048
=> x = 6048 - 5640
=> x = 408
Hence, the distance covered by train = 940 - 408 = 532 km
and time taken = 532/84 hrs
= 133/21 hrs {532 and 84 are divided by 4}
= 19/3 hrs {133 and 21 are divided by 7}
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