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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
2.11 Speed and Distance Word Problems

Steps:
1. Read the problem carefully and note down what is given and what is required.
2. Select a letter letter or variable x or y or z to represent the unknown quantity asked for.
3. Represent the word statements of the problems in the symbolic language step by step.
4. Look for quantities which are equal as per conditions given and form an equation.
5. Solve the equation.
6. Verify the result for making sure that your answer satisfies the requirements of the problems.

Examples:

  1. John walked to school at an average speed of 3 miles an hour and jogged back along the same route at 5 miles an hour. If his total traveling time was 1 hour, what was the total number of miles in the round trip?
    Solution:
    Total distance = Total rate * total time
    Let 'x' be the distance from home to school.
    TimeRateDistance
    To School x/3 3 miles/hr x
    Back x/5 5 miles/hr x
    Total 5 miles/hr 2x
    x/3 + x/5 = 1
    5x + 3x = 15
    8x = 15
    x = 15/8 miles
    Total distance = 2x = 2 (15/8) = 3 3/4
    Answer: 3 3/4

  2. In a stream the current flows at the rate 4 miles/hr. For a boat the time taken to cover a certain distance upstream is 5 times the time it takes to cover the same distance downstream. Find the speed of the boat in still water.
    Solution:
    Let the speed of the boat in still water = x miles/hr.
    Speed of the boat downstream will be greater than its speed in still water, due to favorable current of water.
    \ Speed of the boat downstream = Speed of the boat + Speed of water current.
    = (x+4) miles/hr.
    Speed of the boat upstream will be less than its speed in still water, due to opposing current of water.
    \Speed of the boat upstream = Speed of the boat - Speed of the current.
    = (x-40)miles/hr.
    Let the time taken to cover the distance downstream = t hrs.
    \Time taken to cover distance upstream = 5t hr.
    Now, distance traveled downstream = Speed * Time
    = (x+4)t miles.
    Distance traveled upstream = (x-4)5t miles.
    Since distance traveled both ways are same.
    (x+4)t = (x-4)5t
    Dividing both sides by 't'(¹0).
    (x+4) = 5(x-4)
    x+4 = 5x-20
    Transposing 5x and 4
    5x - x = 20 + 4
    4x = 24
    x = 24/4 = 6
Directions: Solve the following word problems. Write and solve at least four more word problems involving speed and distance.
Q 1: A postman takes letters on foot from city A to city B at a speed of 4 miles/hr. If he walks at a speed of 5 miles/hr, then he reaches the city 7 minutes earlier. Find the distance between the two cities.
5 miles
6/7 miles
7/3 miles

 Q 2: Harry walked to the town at a speed of 4 miles/hr, and came back by bicycle at a speed of 12 miles/hr. The total time for to and fro journey was 5/2 hrs. Find the time taken by him to travel foot.
112.5 minutes
16.5 minutes
11.25 minutes

Question 3: This question is available to subscribers only!

 Question 4: This question is available to subscribers only!


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