# Motion Problem

## 09 - Number of Leaps to Take to Catch the Lead

**Problem**

A cat takes 4 leaps to a dog's 3; but 2 of the dog's leaps are equivalent to 3 of the cat’s. The cat has a start of 50 leaps. How many leaps must the dog take to catch the cat?

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## 08 - Sound of Impact be Heard Before the Report of the Gun

**Problem**

A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.

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## 07 - A Man Covers an Unknown Distance at Different Rates

**Problem**

A man covers the distance *A* to *B* in 5 hours and 30 minutes. During the second half of the distance he traveled 1/2 kilometer less per hour than during the first half. In the return trip from *B* to *A*, by traveling 1 km/hr faster than during the first half of his trip from *A* to *B*, he consumed 3-3/4 hours. Determine the distance *AB*.

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## 06 - The Battleship Was Brought to Full Stop After 1 Hour of Voyage

**Problem**

A battleship started on a 500-mile voyage but was brought to full stop an hour after starting for military reasons, delaying it for full hour, after which it was ordered to proceed at a reduced velocity equivalent to 75% of its former rate. The ship arrived at its destination 3 hours and 3 quarters after scheduled time. If it was desired for the ship to arrive one hour and a quarter sooner, how far from the destination should the ship have been ordered stopped?

## 05 - Two runners moving in opposite directions in a circular track

**Problem**

Benjie and Jerwin is running in opposite directions in a 400-meter circular track and meet each other every 35 seconds. If Benjie can complete one track in 65 seconds. How long does it take for Jerwin to run 400 meters?

## 04 - Two runners moving in the same direction in an oval track

**Problem**

Runners A and B start together in a race around a 900-ft oval track. Runner A is making a speed of 27 ft/sec and runner B at 22.5 ft/sec. How long will it take runner A to be exactly one circumference ahead of runner B.

## 03 - In rowing a boat: find the rate of stream

**Problem**

A man can row 77 km and back in 14 hours. If he can row 6.5 km with the stream at the same time as 4.8 km against the stream, find the rate of the stream.

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## 02 - Cars moving in opposite directions

**Problem**

A car leaves city A for city B, 40 km distant, traveling 50 kph. Thirty minutes later, another car leaves city B for city A at 40 kph. At what point of their path will the first car pass 6 minutes before the second car?

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## 01 - Sound of impact of the bullet hitting the target

**Problem**

A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.