Two motorists left A to B simultaneously. The first drove at a constant speed all the way. The second traveled the first half of the journey at a speed lower than the first by 3 km / h, and the second half of the journey at a speed of 28 km / h, as a result of which he arrived in B simultaneously with the first motorist. Find the speed of the first motorist if it is known to be greater than 20 km / h.
Let x be the speed of the first motorist. By s we denote half of the way between points A and B. Then the time spent by the first motorist for the entire way is 2s hours.
The speed of the second motorist in the first half is x-3, and the time s / x is 3 hours. The speed on the second half of the journey for the second motorist is 28 km / h, therefore, the time was s / 28 hours. Considering that both motorists covered the entire path in the same time, we get the equation:
s / x-3 + s / 28 = 2s / x
1 / x-3 + 1/28 = 2x
28x + x ^ 2-3x = 56 (x-3)
x ^ 2-31x + 168 = 0
We solve the quadratic equation, the roots are obtained:
x1 = 7
x2 = 24
By condition, the speed must be more than 20, respectively, the second answer.
Answer: 24km / h.
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