To travel a distance of 600 km, the slower train takes 4 hrs more than the faster one. However, if the speed of the slower is doubled, it takes 1 hrs less than the faster train. Find the speed of the faster train.
Question
To travel a distance of 600 km, the slower train takes 4 hrs more than the faster one. However, if the speed of the slower is doubled, it takes 1 hrs less than the faster train. Find the speed of the faster train.
Solution
Let's denote the speed of the faster train as F and the speed of the slower train as S.
From the problem, we know that the time it takes for each train to travel 600 km is related to their speeds by the equation:
600/S = 600/F + 4
This equation comes from the fact that the slower train takes 4 hours more than the faster train to travel the same distance.
We also know that if the speed of the slower train is doubled, it takes 1 hour less than the faster train. This gives us a second equation:
600/(2S) = 600/F - 1
We now have a system of two equations, and we can solve for F and S.
First, let's simplify each equation by dividing every term by 600:
1/S = 1/F + 4/600 1/(2S) = 1/F - 1/600
This simplifies to:
1/S = 1/F + 1/150 1/(2S) = 1/F - 1/600
Now, let's subtract the second equation from the first to eliminate F:
1/S - 1/(2S) = 1/150 + 1/600
Solving for S gives:
S = 60 km/hr
Substituting S into the first equation gives:
1/60 = 1/F + 1/150
Solving for F gives:
F = 75 km/hr
So, the speed of the faster train is 75 km/hr.
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