Lesson Simple and simplest arithmetic Travel & Distance problems

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Simple and simplest arithmetic Travel & Distance problems

The problems in this lesson are about a car moving from town A to town B.
The variables we are talking about are the distance between A and B, the rate (the average speed) of the car, and the time traveled.

The general formula is D = V*T, where D is the traveled distance, V is the constant rate (average speed), and T is the time.

If you know and understand this symbolic formula, then you certainly can solve each problem of the lesson.
But even if you do not know the formula, you can solve the problems, because you understand intuitively that

    - the distance traveled is the product of the rate and the time;
    - the time is the quotient of the distance and the average rate;
    - the average rate is the quotient of the distance and the time.

By knowing these simple rules, you can solve many word problems of this class.

Problem 1

A car moves from A to B at the rate of 60 miles per hour.
It took 4 hours to reach B. Find the distance from A to B.

Solution

The distance is the product of the time and the average rate: D = V*T.


At given data the distance is D = 4 hours * 60  = 240 miles.


ANSWER.  The distance is 240 miles.

Problem 2

The distance between the cities A and B is 195 miles. A car moves from A to B
at the rate of 65 miles per hour. How long will it take for the car to reach B?

Solution

The time to reach B is  T = ,  where D is the distance, V is the car's rate.


At given conditions, it will take   = 3 hours to reach B.


ANSWER.  At given conditions, it will take 3 hours for the carto reach B.

Problem 3

The distance between the cities A and B is 300 miles.
A car covered the distance from A to B in 5 hours. Find the average speed of the car.

Solution

The average speed is  V = ,  where  D is the distance and T is the time traveled.


At given conditions, the average speed of the car is V =  = 60 miles per hour.


ANSWER. At given conditions, the average speed of the car is 60 miles per hour.

Problem 4

A driver travels 288 miles in 6 hours. What is the average speed, in miles per hour?

Solution

To find the average speed, divide the distance by the time.


You will get then  


    the average speed =  = 48 miles per hour.    ANSWER

Problem 5

Two cars entered an Interstate highway at the same time and traveled toward each other
The initial distance between the cars was 390 miles. The first car was running
at the speed 70 miles per hour, the second car was running at 60 miles per hour.
How long will it take for the two cars to pass each other?

Solution

Since the cars move toward each other, the distance between them decreases at the rate of  70 + 60 = 130 miles per hour.

Therefore, the time before they meet each other is the distance divided by the approaching rate, i.e.  =  = 3 hours.    ANSWER

Problem 6

Two motorcycles travel toward each other from cities that are about 950 km apart at rates of 100 km/h and 90 km/h.
They started at the same time. In how many hours will they meet?

Solution

Since the motorcyclists move toward each other, the distance between them decreases at the rate of 100 + 90 = 190 miles per hour.

Therefore, the time before they meet each other is the distance divided by the approaching rate, i.e.  =  = 5 hours.    ANSWER

Problem 7

Two planes start from the same point and fly in opposite directions. One travels at 475 mi/h and the other at 525 mi/h.
How long will it take before they are 3000 miles apart?

Solution

Since the planes fly in opposite directions, the distance between them increases at the rate of 475 + 525 = 1000 miles per hour.

Therefore, the time before they will be 3000 miles apart is the distance divided by the rate moving away from each other, i.e.  =  = 3 hours.    ANSWER

Problem 8

Ming left the hospital at the same time as Adam. They drove in opposite directions.
Adam drove at a speed of 50 km. After two hours they were 180 km apart. How fast did Ming drive ?

Solution

In two hours, Adam traveled 2*50 = 100 kilometers.


Hence, Ming traveled 180-100 = 80 kilometers in 2 hours.


So, the Ming's average speed was  80/2 = 40 kilometers per hour.    ANSWER

My other lessons on arithmetic word problems in this site are
    Arithmetic word problems to solve them MENTALLY
    Solving arithmetic word problems by reasoning
    Simple arithmetic word problems solved in a right way
    Arithmetic coin problems
    Simple arithmetic word problems on "rate of work"
    Typical arithmetic Travel & Distance problems
    Entertaining catching up arithmetic Travel & Distance problems
    Other basic arithmetic Travel & Distance problems
    Advanced arithmetic word problems on Travel & Distance
    Finding travel time and average rate
    Flying back and forth

    OVERVIEW of the first group of lessons on arithmetic word problems

To see the whole list of lessons on arithmetic problems, use this link Arithmetic problems - YOUR ONLINE TEXTBOOK
It is your way to the entry page of the online textbook on Arithmetic problems.

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