Two cyclists left one village for another at the same time. the speed of the first cyclist is 5 km h less

| May 13, 2021 | education

Two cyclists left one village for another at the same time. the speed of the first cyclist is 5 km h less than the speed of the second. Find the speed of the second cyclist if he arrived 12 minutes earlier than the first, and the distance between villages is 12 km.

Let’s record the speed of the first cyclist as x km / h.

Since it is 5 km / h less than the speed of the second, the speed of cyclist 2 will be equal to: x + 5.

We translate the time value from minutes to hours.

12 minutes = 12/60 = 1/5 = 0.2 hours.

We get the equation:

12 / x – 12 / (x + 5) = 0.2.

12 * x + 60 – 12 * x = 0.2 * x ^ 2 + x.

0.2 * x ^ 2 + x – 60 = 0.

D ^ 2 = 1 – 4 * 0.2 * (-60) = 1 + 48 = 49.

D = 7.

x = (-1 + 7) / 2 * 0.2 = 6 / 0.4 = 15 km / h (speed of 1 cyclist).

x + 5 = 15 + 5 = 20 km / h (speed of 2 cyclists).

Answer: 20 km / h.



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