Two trains travel between two stations 80 km apart. If train A travels at an averagespeed of 5 km/h faster than train B and completes the journey 20 minutes faster, find theaverage speeds of the two trains, giving your answers correct to two decimal places.
Question
Two trains travel between two stations 80 km apart. If train A travels at an averagespeed of 5 km/h faster than train B and completes the journey 20 minutes faster, find theaverage speeds of the two trains, giving your answers correct to two decimal places.
Solution
Let's denote the speed of train B as x km/h. Therefore, the speed of train A is x + 5 km/h.
The time it takes for each train to travel between the two stations can be found using the formula time = distance/speed.
So, the time for train B is 80/x hours and the time for train A is 80/(x+5) hours.
According to the problem, train A completes the journey 20 minutes (or 1/3 of an hour) faster than train B. So we can write the equation:
80/x - 80/(x+5) = 1/3
To solve this equation, we first multiply each term by 3x(x+5) to get rid of the fractions:
240(x+5) - 240x = x(x+5)
Expanding and simplifying gives:
1200 = x^2 + 5x
Rearranging into a quadratic equation gives:
x^2 + 5x - 1200 = 0
This can be factored into:
(x - 30)(x + 40) = 0
The solutions to this equation are x = 30 and x = -40. Since speed cannot be negative, we discard x = -40.
So, the speed of train B is 30 km/h and the speed of train A is 30 + 5 = 35 km/h.
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