A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km per hour less than the speed of the faster train, then, find the speed of the two trains.

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Detailed Solution

Concept- Remember how to calculate speed in terms of distance and time. Give the two trains' speeds variables, then locate the two equations that connect them to the available data. To determine the train's speed, solve the equations.
There are two trains; the rapid train is one and the slow train is the other.
Let the faster train's speed be x and the slower train's speed be y.
The following is the formula for speed v in relation to distance d and time t:

The following formula provides the time taken in terms of speed and distance:

Given is the amount of time needed for the fast train to travel 600 kilometres.

Given is the amount of time needed for the slow train to travel 600 kilometres.

Since the fast train travels at a speed of three hours faster than the slow train, we have:

Equations (1) and (2) are replaced, and the result is:

Given that the fast train moves at a speed that is 10 km/h more than the slow train's, we have:

Writing x as a function of y gives us:

Equation (3) becomes: when equation (4) is substituted for it.

Cross multiplying, we have:

To put it simply, we have:

When we solve for y, we get:
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The train's speed is a positive number.