Question

Водитель проехал первые 40% пути со скоростью, на 20% меньшей запланированной. На сколько процентов он должен увеличить свою фактическую скорость на оставшемся участке пути, чтобы в итоге весь путь был пройден на 2% быстрее, чем планировалось?

Answer 1

Путь/скорость=время
40%=0,4 от всего пути.
100%-20%=80%=0,8 - скорость на первых 40% пути
0,4/0,8=0,5    50% времени было затрачено на проезд первых 40% пути.
у него осталось времени 1-0,5-0,03125=0,46875
осталось проехать пути 1-0,4=0,6

путь/время=скорость
0,6/0,46875=1,28
1,28-1=28%
Ответ: на 28%

Answer 2

Calculation of the Required Increase in Speed

To determine the percentage by which the driver needs to increase their actual speed on the remaining portion of the journey in order to complete the entire distance 2% faster than planned, we can follow these steps:

1. Let's assume the total distance of the journey is represented by 100%. 2. The driver has already traveled the first 40% of the distance at a speed that is 20% slower than planned. 3. This means the driver has covered 40% of the distance at 80% of the planned speed. 4. To find out how much faster the driver needs to go on the remaining 60% of the distance, we can set up the following equation:

40% x 80% + 60% x (100% + x%) = 100%

Here, x% represents the required increase in speed on the remaining portion of the journey.

5. Solving the equation for x%, we can find the answer.

Calculation:

Let's solve the equation to find the required increase in speed:

40% x 80% + 60% x (100% + x%) = 100%

Simplifying the equation:

32% + 60% x (100% + x%) = 100%

Expanding the equation:

32% + 60% + 60% x x% = 100%

Combining like terms:

92% + 60% x x% = 100%

Subtracting 92% from both sides:

60% x x% = 8%

Dividing both sides by 60%:

x% = 8% / 60%

Calculating the value of x%:

x% = 0.1333...

Converting x% to a percentage:

x% ≈ 13.33%

Answer:

To complete the entire distance 2% faster than planned, the driver needs to increase their actual speed on the remaining portion of the journey by approximately 13.33%.