Question

Теплоход проходит по течению реки до пункта назначения 140 км и после стоянки возвращается в пункт отправления. Найдите скорость теплохода в неподвижной воде, если скорость течения равна 5 км/ч, стоянка длится 11 часов, а в пункт отправления теплоход возвращается через 32 часа после отплытия из него.

Answer 1

Х-собственная скорость,время движения 32-11=21ч
140/(х+5)+140/(х-5)=21
Разделим каждое на 7
20/(х+5)+20/(х-5)=3
х≠5 и х≠-5
3х²-75-20(х-5+х+5)=0
3х²-40х-75=0
D=1600+900=2500
x1=(40-50)/6=-5/3-не удов усл
х2=(40+50)/6=90/6=15км/ч-собственная скорость

Answer 2

Problem Analysis

We are given the following information: - The distance from the starting point to the destination is 140 km. - The speed of the current is 5 km/h. - The duration of the stop at the destination is 11 hours. - The return journey from the destination to the starting point takes 32 hours.

We need to find the speed of the boat in still water.

Solution

To find the speed of the boat in still water, we can use the formula:

Speed of boat in still water = (Distance traveled)/(Time taken)

Let's calculate the speed of the boat in still water step by step.

1. Calculate the total time taken for the round trip: - Time taken from the starting point to the destination: 140 km / (Speed of boat in still water + Speed of current) - Time taken for the stop at the destination: 11 hours - Time taken from the destination to the starting point: 140 km / (Speed of boat in still water - Speed of current) - Total time taken for the round trip: Time taken from the starting point to the destination + Time taken for the stop at the destination + Time taken from the destination to the starting point + 32 hours

2. Calculate the speed of the boat in still water using the formula: - Speed of boat in still water = 140 km / (Total time taken for the round trip)

Let's calculate the speed of the boat in still water using the given information.

Calculation

1. Calculate the total time taken for the round trip: - Time taken from the starting point to the destination: