Rate Problems With Fractions

Rate is a measure of the quantity of something in relation to another quantity, typically expressed as a ratio, fraction, or percentage. It represents how one quantity changes with respect to another quantity.

In general, the rate can be defined as the amount of change in one quantity with respect to another quantity, often over a specific unit of time or other standard unit of measurement.

Rate problems involve calculating quantities such as speed, distance, time, or work done based on given rates. These problems often involve the relationship between two or more quantities, typically expressed as a rate or ratio.

Example Questions 

1. A water tank can be filled by Pipe A in 3/4 of an hour and by Pipe B in 5/6 of an hour. If both pipes are opened simultaneously, how long will it take to fill the tank?

Solution

Let t be the time it takes to fill the tank when both pipes are opened simultaneously.

The rates at which Pipe A and Pipe B fill the tank are 1/(3/4) = 4/3 tanks per hour and 1/(5/6) = 6/5 tanks per hour respectively.

When both pipes are opened simultaneously, their combined rate is the sum of their individual rates:

Combined Rate = 4/3 + 6/5 = 20/15 + 18/15 = 38/15

Now, we can set up the equation:

38/15 x t = 1

=> t = 1 x 15/38 = 15/38 hours

2. A car travels at a speed of 3/4 of a mile per minute. How far will it travel in 5/6 of an hour?

Solution

First, we need to convert 5/6 of an hour into minutes since the speed is given in miles per minute.

Given that there are 60 minutes in an hour:

5/6 of an hour = 5/6 x 60 = 50 minutes

The distance the car travels is given by the rate multiplied by the time:

Distance = speed x time

Given that the speed is 3/4 of a mile per minute, and the time is 50 minutes, we have:

Distance = 3/4 x 50 = 150/4 = 37.5 miles in 5/6 of an hour.

3. A faucet can fill a bathtub in 3/8 of an hour. If the faucet is left running, how much of the bathtub will be filled in 1/4 of an hour?

Solution

The portion of the bathtub filled in 1/4 of an hour is given by the rate multiplied by the time:

Portion filled = 1/4 x 3/8 = 3/32 of the bathtub

So, 3/32 of the bathtub will be filled in 1/4 of an hour

4. A train travels at a speed of 3/5 of a mile per minute. How long will it take the train to travel a distance of 4/3 miles, in hours?

Solution

Distance = Speed x time

=> Time = Distance/Speed

= (4/3)/(3/5)

= 4/3 x 5/3

= 20/9

So, the time taken by the train to travel a distance of 4/3 miles is 20/9 minutes = (20/9)/60 hours = 1/27 hours

Rate Problems With Fractions FAQS

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