Mathematics
A train covered a certain distance at a uniform speed. If the train had been 30 km/h faster, it would have taken 2 hours less than scheduled time. If the train were slower by 15km/h , it would have taken 2 hours more than the scheduled time. Find the length of the journey.
Linear Equations
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Answer
Let the actual speed of the train be x km/h and scheduled time be y hours.
Distance = Speed × Time = xy.
According to first condition,
⇒ (x + 30)(y - 2) = xy
⇒ xy - 2x + 30y - 60 = xy
⇒ -2x + 30y = 60 ……(i)
According to second condition,
⇒ (x - 15)(y + 2) = xy
⇒ xy - 15y + 2x - 30 = xy
⇒ 2x - 15y = 30 …….(ii)
Adding (i) and (ii) we get,
(-2x + 30y) + (2x - 15y) = 60 + 30
15y = 90
y = 6.
Substituting value of y in (i) we get,
⇒ -2x + 30(6) = 60
⇒ -2x + 180 = 60
⇒ -2x = -120
⇒ x = 60.
Distance = xy = 60 × 6 = 360 km.
Hence, distance of journey = 360 km.
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