A train covers a certain distance at a uniform speed. If the train had been 10 km/hr faster it would have taken 2 hours less than the scheduled time. If the train was slower by 10 km/hr it would have taken 3 hours more than the scheduled time. Write the two equations.
Let the speed of train be s km/hr as for “d” km it would take “t” hr.
We know that, Distance = Speed × Time
Therefore, d = s × t
According to question, for the same distance d,if speed increases by 10km/hr
time will decrease by 2hr,i. e,
⇒ d = (s + 10)(t – 2)
⇒ d = st – 2s + 10t – 20
⇒ 2s – 10t = – 20
⇒ s – 5t = – 10 ……(i)
Also, for the same distance d, if speed decreases by 10/hr time will increase by 3hr,i. e,
⇒ d = (s – 10)(t + 3)
⇒ d = st + 3s – 10t – 30
⇒ 3s – 10t = 30 …… (ii)
(i)&(ii) are the required equations.
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