Simple distance traveled problem

In summary, the problem involves a boy walking and running at different speeds to and from his school, with a total travel time of 1 hour. To solve, one must set up equations for the distance traveled at each speed and then solve for the total distance. By redefining a variable, the solution is found to be 3.75 miles.
  • #1
Elbobo
145
0

Homework Statement


A boy walks at an average speed of 3 miles per hour to his school, and then runs back at an average speed of 5 miles per hour along the same route. The total travel time is 1 hour. What was the total distance traveled?

The Attempt at a Solution


OK it's a practice question I saw in my SAT prep book, and I feel soooo incredibly stupid to not be a ble to solve this. The answer is 3.75 miles, btw.

d1 = d2
dt = d1 + d2
t1 + t2 = 1 hr
d1 = v1t1
d2 = v2(1-t1)

dt = v1t1 + v2-v2t1
dt = 3t1 + 5 - 5t1

Then I get stuck here.

Pretty sure I am over complicating the problem, so could somene help me?
 
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  • #2
Let the distance to school be d. Then d/v1+d/v2=1hr. Solve for d. The total distance traveled is then 2*d.
 
Last edited:
  • #3
Ohh, ok I didn't think about redefining t1.

Thanks.
 

What is a simple distance traveled problem?

A simple distance traveled problem is a type of mathematical problem that involves calculating the distance traveled by an object, given its speed and time traveled. It is commonly used in physics and engineering to determine the position of an object at a specific time.

What are the key components of a simple distance traveled problem?

The key components of a simple distance traveled problem are the speed of the object, the time it has traveled, and the distance it has traveled. These three variables are used to calculate the unknown distance, using the formula distance = speed x time.

How do I solve a simple distance traveled problem?

To solve a simple distance traveled problem, you need to have two of the three variables (speed, time, and distance) and use the formula distance = speed x time. Plug in the known values and solve for the unknown variable.

What are some real-life applications of simple distance traveled problems?

Simple distance traveled problems have many real-life applications, such as calculating the distance traveled by a car on a road trip, determining the velocity of a moving object, and predicting the position of a spacecraft in space.

What are some common mistakes made when solving a simple distance traveled problem?

Some common mistakes when solving a simple distance traveled problem include using the wrong units of measurement, not converting units correctly, and forgetting to include the units in the final answer. It is also important to double-check your calculations to ensure accuracy.

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