Jordan rode his bike along a trail at an average speed of 12 miles per hour for hours. He then continued along the same trail on foot, walking at an average speed of 4 miles per hour for 3 hours. The total distance he traveled was 36 miles.
What is the value of ?
A trip with different speeds is a rate problem: miles per hour tells you how many miles are covered in one hour. Multiply each speed by its own travel time, then add the two distances to match the total. Solve the resulting equation in Desmos. Dividing the whole trip’s distance by the biking speed ignores the miles traveled on foot.
Hints
- Hint 1
A rate in miles per hour tells you the distance covered in one hour. Multiply the biking rate by the time spent biking to write the biking distance in terms of .
- Hint 2
Walking has its own time, separate from the biking time. Multiply the walking speed by its time to find the walking distance. What must the two distances add up to?
Step-by-step
Add the distances, then solve
Step 1Find the biking distance
The biking rate is miles in one hour, so multiply it by the biking hours to get the biking distance: .
- Step 2
Find the walking distance
Walking lasts hours, not hours. Multiply the walking speed by that time to get the walking distance: .
- Step 3
Write the total-distance equation
Both results are distances in miles, so add the distances from both parts and set them equal to the total of miles: . Adding the speeds instead would not account for how long Jordan traveled at each speed.
- Step 4
Solve for the biking time
To find the biking hours, type in Desmos. Use instead of so Desmos solves for the unknown rather than graphing it; tells Desmos to match the two sides. Under PARAMETERS, it shows . So Jordan biked for hours. Choice B.