Linear Equations

Linear Equations: Level 3 Challenges


A man wants to climb a pole 50m tall pole. At first, he first climbs 1m but slides down 1m back to the ground. Then, he climbs 2m, but slides down 1m. Then, he climbs 3m, but slides down by 1m. Then, he climbs 4m, but slides down by 1m, and so on.

If the man spends 10 seconds for each meter he climbs up and 5 seconds for each meter he slides down, then how many seconds will it take him to reach the top of the pole?

Image credit: Wikipedia Ross

Rooney, Hernandez, and Robin race each other in a 100 meter race. All of them run at a constant speed throughout the race.

If Rooney beats Hernandez by 20 meters and Hernandez beats Robin by 20 meters, then by how many meters does Rooney beat Robin?

A thief escapes from a prison. When he was at a distance of 5km from the prison, the police start chasing him with a speed of 20m/s. The thief is running away with speed 10m/s. A police dog starts running as soon as the police starts, with a speed of 30m/s and runs back and forth from the police to the thief and back to the police till the police catch the thief.

In kilometers, find the distance that the dog ran in the forward direction only.

My watch is 1 second fast per hour and James's is 1.5 seconds slow per hour. Right now they show the same time. In how many minutes later will they show the same time again?

The average age of the members of a 10-person committee is the same as it was 4 years ago, because an old member has just been replaced by a new member.

How much younger is the new member than the old member who was replaced?


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