There are two different roads between two cities. The first is 20km longer than the second. A car travels along the first road and covers the distance between the cities in 312 hours. Another car travels along the second road and covers the distance in 212 hours. If the speed of the first car is 40km/hr less than that of second car, then what is the speed of faster car ?
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Answer:
Speed of car = x km/hr
Speed of train = (x+16) km/hr
And, we know that
Time = Distance / Speed
(i) Time taken by the car to reach town B from town A = 216/x hrs
(ii) Time taken by the train to reach town B from town A = 208/(x+16) hrs
(iii) According to the question, we have
x
216
=
x+16
208
=2
x(x+16)
216x+3456−208x
=2
x(x+16)
8x+3456
=2
4x+1728=x
2
+16x
x
2
+12x−1728=0
x(x+48)−36(x+48)=0
(x+48)(x−36)=0
x=−48,36
As speed cannot be negative,
=36
(iv) Therefore, the speed of the train is (x+16)=(36+16) km/hr = 52 km/h
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