Question

Joseph and sandra start biking down the redstone trail at the same time. joseph starts at an entry point 0.5 miles from the top of the trail and bikes downhill at a speed of 14 miles per hour. sandra starts 2.6 miles from the top of the trail and bikes downhill at a speed of 10.5 miles per hour. which equation can you use to find h, the number of hours it will take for joseph to catch up to sandra? how long will it take for joseph to catch up to sandra? simplify any fractions.

Answer 1

To determine the time for Joseph to catch up to Sandra, set up an equation reflecting their distances traveled. After solving the equation 14h = 10.5h + 2.1, we find that Joseph will catch up to Sandra in 0.6 hours, or 36 minutes.

Step-by-step explanation:

To find h, the number of hours it will take for Joseph to catch up to Sandra, we need to set up an equation that represents the total distance each person has traveled. Since they both start at different points and travel the same trail, we want to set their distances equal to each other once Joseph catches up to Sandra.

The distance that Joseph travels is his speed (14 mph) multiplied by the time (h). Sandra's distance is slightly more complex. She already has a 2.1-mile head start (2.6 miles - 0.5 miles that Joseph is behind), and also travels at her speed (10.5 mph) multiplied by time (h).

The equation representing the moment Joseph catches up to Sandra is:

14h = 10.5h + 2.1

Now, simplify the equation:

Subtract 10.5h from both sides to get 3.5h = 2.1.

Divide both sides by 3.5 to find h.

h = 2.1 / 3.5, which simplifies to h = 0.6 hours.

Therefore, Joseph will take 0.6 hours or 36 minutes to catch up to Sandra.