A passenger train running at a speed of 80km/h leaves a railway station 6 hours after a goods train leaves and overtakes it in 4 hours . what is the speed of the goods train?
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Also, by the time the train is overtaken, the passenger train should have travelled the same distance as the goods train. It is given that the speed of the passenger train is 80 km/hr and time taken is 4 hours. Therefore, the speed of the good train is 32 km/hr. Hence, the answer is option (c).
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CBSE
Mathematics
Grade 8
Speed Distance and Time
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A passenger train running at a speed of 80km/hr leaves the railway station 6 hours after a good train leaves and overtakes it is 4 hours. What is the speed of the good train goods train?
(a) 48 km/hr
(b) 60 km/hr
(c) 32 km/hr
(d) 80 km/hr
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Hint: Let the speed of the good train be x km/hr. Now when the good train is overtaken, it has travelled for a total time of 10 hours, so using the formula distance=speed×time we can say that distance is equal to 10x km. The passenger train has to cover the same distance in 4 hours to overtake it. So, again using the same formula we can say distance is equal to 80×4 km . Equate the two distances to get the answer.
Complete step-by-step answer:
Let the speed of the good train be x km/hr.
Now when the good train is overtaken, it has travelled for a total time of 10 hours,as it started 6 hours early and took 4 hours to be overtaken. So, the distance travelled by is:
distance=speed×time=10x km
Also, by the time the train is overtaken, the passenger train should have travelled the same distance as the goods train. It is given that the speed of the passenger train is 80 km/hr and time taken is 4 hours.
distance=speed×time=80×4=320 km
Now, we will equate the two distances that we found in the above case, we get
10x=320
x=32 km/hr