Question

Два мотоциклиста выезжают одновременно в город из пункта отстоящего от него на 160 км. Скорость первого мотоциклиста на 8 км/ч больше скорости второго, поэтому он приезжает к месту назначения на 40 мин раньше. Найдите скорость второго мотоциклиста.

Answer 1

может быть так:

скорость 1 = х км/ч, а 2 =  у км/ч. 
Значит: х=у+8 или х-у=8. 
Далее:-160/х + 160/у = 2/3 
Получается:х-у=8 
-160/х + 160/у = 2/3  
-160/(8+у) + 160/у = 2/3
-160у+160(у+8)=2у(у+8)/3
-160*3у+160*3у+1280*3=2у^2+16у 
2у^2+16у-3840=0 
 у=40 => х=48 
у=-48 - не возможно, скорость не может быть отрицательной

Answer 2

Problem Analysis

We are given that two motorcyclists start simultaneously from a point that is 160 km away from the city. The first motorcyclist's speed is 8 km/h faster than the second motorcyclist. The first motorcyclist arrives at the destination 40 minutes earlier than the second motorcyclist. We need to find the speed of the second motorcyclist.

Solution

Let's assume the speed of the second motorcyclist is x km/h. Then the speed of the first motorcyclist would be x + 8 km/h.

We know that the distance traveled by both motorcyclists is the same, which is 160 km.

We can use the formula distance = speed × time to calculate the time taken by each motorcyclist.

For the first motorcyclist: - Distance = 160 km - Speed = x + 8 km/h - Time = 160 / (x + 8) hours

For the second motorcyclist: - Distance = 160 km - Speed = x km/h - Time = 160 / x hours

We are given that the first motorcyclist arrives 40 minutes earlier than the second motorcyclist. Since 40 minutes is equal to 40/60 = 2/3 hours, we can set up the following equation:

160 / (x + 8) = 160 / x + 2/3

To solve this equation, we can cross-multiply and simplify:

160x = 160(x + 8) + 2/3x(x + 8)

Simplifying further:

160x = 160x + 1280 + 2/3x^2 + 16x

Combining like terms:

0 = 2/3x^2 + 16x + 1280

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2/3, b = 16, and c = 1280. Plugging in these values, we can calculate the value of x, which represents the speed of the second motorcyclist.

Let's calculate the value of x using the quadratic formula.