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Solving the Distance-Rate-Time Problem: Determining the Speeds of Two Airplanes, Lecture notes of Physics

Northumbria UniversityPhysics

A step-by-step solution to the distance-rate-time problem, where two airplanes travel in opposite directions with a given difference in speed and distance apart after a certain time. The document uses the distance-rate-time formula and algebraic substitution to find the speeds of both planes.

What you will learn

  • What algebraic method is used to solve the two equations in the Distance-Rate-Time Problem?
  • What is the speed of each airplane in the Distance-Rate-Time Problem?
  • How can the Distance-Rate-Time formula be used to find the speeds of two airplanes?

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Distance-Rate-Time Problem LSC-O 6/2010, Rev. 1/2011
1 of 2
Instructions Example
1. Carefully read the problem, note
what numerical data is given,
and what is being asked for.
Two airplanes depart from an airport
simultaneously, one flying 100 km/hr
faster than the other. These planes travel
in opposite directions, and after 1.5
hours they are 1275 km apart.
Determine the speed of each plane.
2. Make a sketch, drawing, or
picture of the described
situation, and put all the given
data from the problem on the
drawing.
Look for what the problem’s
question is. In other words,
what do they want to know? In
this example, the problem asks
you to find the speed of each
plane.
Let x = the speed of one plane,
and y = the speed of the other.
3. Write down any numerical
relationships that the problem
gives you: Distance apart is
1275 km, time traveled is 1.5
hrs, and one plane is traveling
100 m/hr. faster than the other.
Let plane X be the faster plane.
4. Look for other information
(numbers, formulas, etc.) that
you can use to relate all the
items.
Distance = Rate • Time is the
formula you need in this case.
Distance traveled = Rate (or Speed) times
Time.
1275 km is the total of the distances
(added together) that each plan travels.
Travel time for each plane is the same, 1.5
hours; however, the planes’ speeds differ
by 100 km/hr.
Plane X
is traveling
X m/hr.
Plane Y
Is traveling
Y m/hr.
1275 km
in 1.5 hours
Speed of
Plane Y is
100 m/hr
slower than X.
Speed of
Plane X is
100 m/hr
faster than Y.
pf2

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Distance-Rate-Time Problem LSC-O 6/2010, Rev. 1/

1 of 2

Instructions Example

  1. Carefully read the problem, note what numerical data is given, and what is being asked for.

Two airplanes depart from an airport simultaneously, one flying 100 km/hr faster than the other. These planes travel in opposite directions, and after 1. hours they are 1275 km apart. Determine the speed of each plane.

  1. Make a sketch, drawing, or picture of the described situation, and put all the given data from the problem on the drawing. Look for what the problem’s question is. In other words, what do they want to know? In this example, the problem asks you to find the speed of each plane. Let x = the speed of one plane, and y = the speed of the other.

3. Write down any numerical

relationships that the problem gives you: Distance apart is 1275 km, time traveled is 1. hrs, and one plane is traveling 100 m/hr. faster than the other. Let plane X be the faster plane.

  1. Look for other information (numbers, formulas, etc.) that you can use to relate all the items. Distance = Rate • Time is the formula you need in this case.

Distance traveled = Rate (or Speed ) times Time.

1275 km is the total of the distances (added together) that each plan travels. Travel time for each plane is the same, 1. hours; however, the planes’ speeds differ by 100 km/hr.

Plane X is traveling X m/hr.

Plane Y Is traveling Y m/hr.

1275 km in 1.5 hours

Speed of Plane Y is 100 m/hr slower than X.

Speed of Plane X is 100 m/hr faster than Y.

Distance-Rate-Time Problem LSC-O 6/2010, Rev. 1/

2 of 2

  1. Write the DRT formula and an equation showing the difference in the speeds of the two planes; fill in all givens and unknowns.

D = R • T

1275 km = plane X’s distance plus plane Y’s distance: DTotal (or 1275) = Dx + D (^) y Plane X’s distance is its speed x times 1.5, and plane Y’s distance is its speed y times 1.5: 1275 km = (X)(1.5) + (Y)(1.5)

The difference in the planes’ speeds can be expressed as: X – Y = 100

  1. Solve for x and y: This problem involves two equations with two unknowns, so one method to solve it is by using substitution.

From above, the first equation is: 1275 = 1.5X +1.5Y

The second Equation is: X – Y = 100 On this equation, solve for X by adding Y to both sides: X – Y + Y = 100 + Y X = 100 + Y

Substitute back into the first equation: 1275 = 1.5(100 + Y) + 1.5Y 1275 = 150 + 1.5Y + 1.5Y 1275 = 150 + 3Y 1275 – 150 = 150 – 150 + 3Y 1125 = 3Y

3

1125 = 3

3 Y

375 = Y

And then, back into the second equation: X = 100 + Y X = 100 + 375 X = 475 Answer: The faster plane (plane X) is flying 475 km/hr, and the slower plane (plane Y) is flying 375 km/hr.