Question: A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
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Solution:
Let the speed of the train be \(x \text{km/h}\), time be \(t \text{hours}\), and the distance be \(d \text{km}\)
\[
d = x \times t \quad \text{(i)}
\]
Case 1: Speed is \(x + 10 \text{km/h}\) and time is \(t – 2 \text{hours}\)
\[
-2x + 10t = 20 \quad \text{(ii)}
\]
Case 2: Speed is \(x – 10 \text{km/h}\) and time is \(t + 3 \text{hours}\)
\[
3x – 10t = 30 \quad \text{(iii)}
\]
Adding equations (ii) and (iii) to solve for \(x\)
\[
x = 50 \text{km/h}
\]
Substituting the value of \(x\) into equation (ii) to find \(t\)
\[
10t = 120 \Rightarrow t = 12 \text{hours}
\]
Substituting the value of \(t\) and \(x\) into equation (i) to find \(d\)
\[
d = 12 \times 50 = 600 \text{Km}
\]
Hence, the distance covered by the train is 600km.