# Task 2.

At the time when a lion cub, located 6 minutes away, set off for a waterhole, the second, having quenched his thirst, started back along the same path 1.5 times faster than the first. At the same time, a turtle, located 32 minutes away, set off for the waterhole along the same path. After some time, the first lion cub stepped on the turtle, and 2 minutes and 24 seconds later, the second lion cub did the same. How many minutes after the second incident did the turtle reach the waterhole, given that all three moved at constant speeds?

## B-2

At the time when a lion cub, located 5 minutes away, set off for a waterhole, the second, having quenched his thirst, started back along the same path 1.5 times faster than the first. At the same time, a turtle, located 33 minutes away, set off for the waterhole along the same path. After some time, the first lion cub stepped on the turtle, and 3 minutes and 54 seconds later, the second lion cub did the same. How many minutes after the second incident did the turtle reach the waterhole, given that all three moved at constant speeds?

## B-3

At the time when a lion cub, located 6 minutes away, set off for a waterhole, the second, having quenched his thirst, started back along the same path 2 times faster than the first. At the same time, a turtle, located 33 minutes away, set off for the waterhole along the same path. After some time, the first lion cub stepped on the turtle, and 42 seconds later, the second lion cub did the same. How many minutes after the second incident did the turtle reach the waterhole, given that all three moved at constant speeds?

## B-4

At the time when a lion cub, located 5 minutes away, set off for a waterhole, the second, having quenched his thirst, started back along the same path 2 times faster than the first. At the same time, a turtle, located 36 minutes away, set off for the waterhole along the same path. After some time, the first lion cub stepped on the turtle, and 2 minutes and 34 seconds later, the second lion cub did the same. How many minutes after the second incident did the turtle reach the waterhole, given that all three moved at constant speeds?

## B-5

A crocodile swam across a river 30 meters wide in a straight line in 6 seconds. During this time, it was carried 36 meters downstream. After resting and regaining strength, it returned to the same point along the same straight line, but this time fighting the current, in 10 seconds. How many seconds would it take for the crocodile to swim the same distance in still water? Round the answer to the nearest hundredth.

## B-6

A crocodile swam across a river 30 meters wide in a straight line in 6 seconds. During this time, it was carried 24 meters downstream. After resting and regaining strength, it returned to the same point along the same straight line, but this time fighting the current, in 15 seconds. How many seconds would it take for the crocodile to swim the same distance in still water? Round the answer to the nearest hundredth.

## B-7

A crocodile swam across a river 36 meters wide in a straight line in 6 seconds. During this time, it was carried 24 meters downstream. After resting and regaining strength, it returned to the same point along the same straight line, but this time fighting the current, in 9 seconds. How many seconds would it take for the crocodile to swim the same distance in still water? Round the answer to the nearest hundredth.

## B-8

A crocodile swam across a river 56 meters wide in a straight line in 8 seconds. During this time, it was carried 42 meters downstream. After resting and regaining strength, it returned to the same point along the same straight line, but this time fighting the current, in 14 seconds. How many seconds would it take for the crocodile to swim the same distance in still water? Round the answer to the nearest hundredth.
Answer: 9.57

## B-9

A crocodile swam across a river 42 m wide in a straight line in 6 seconds. During this time, it was carried downstream by 28 m. After resting and regaining strength, it returned to the same point along the same straight line, but this time fighting the current, in 14 seconds. How many seconds would it take him to swim the same distance in still water? Round the answer to the hundredths.

## B-10

A crocodile swam across a river 36 m wide in a straight line in 6 seconds. During this time, it was carried downstream by 27 m. After resting and regaining strength, it returned to the same point along the same straight line, but this time fighting the current, in 12 seconds. How many seconds would it take him to swim the same distance in still water? Round the answer to the hundredths.

## Lomonosov School Olympiad in Mathematics

Preliminary Stage 2020/21 Academic Year for 10-11 Grades

## B-1

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