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? Choices: (A)0.5 + 14h = 2.6 + 10.5h (B)14 + 0.5h = 10.5 + 2.6h How long will it take for Joseph to catch up to Sandra? Simplify any fractions. ____ hours

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?   Choices: (A)0.5 + 14h = 2.6 + 10.5h (B)14 + 0.5h = 10.5 + 2.6h  How long will it take for Joseph to catch up to Sandra? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set Up Equation: To find the correct equation, we need to set up an equation that represents the distance each person will travel until Joseph catches up to Sandra. Since they start at different points on the trail, we need to account for their starting positions and their speeds.Joseph's Distance: Joseph starts 0.5 miles from the top of the trail and travels at 14 miles per hour. So, the distance Joseph travels is 0.5 miles plus 14 miles for every hour (h) he bikes.Sandra's Distance: Sandra starts 2.6 miles from the top of the trail and travels at 10.5 miles per hour. So, the distance Sandra travels is 2.6 miles plus 10.5 miles for every hour (h) she bikes.Equation Representation: Joseph will catch up to Sandra when they have both traveled the same distance. Therefore, the equation to represent this situation is: 0.5 + 14h = 2.6 + 10.5h This is choice (A).Solve for h: Now, we need to solve the equation for h to find out how long it will take for Joseph to catch up to Sandra. 0.5 + 14h = 2.6 + 10.5h Subtract 10.5h from both sides to get the h terms on one side: 0.5 + 14h - 10.5h = 2.6 + 10.5h - 10.5hIsolate h Term: Simplify the equation: 0.5 + 3.5h = 2.6 Now, subtract 0.5 from both sides to isolate the term with h: 0.5 + 3.5h - 0.5 = 2.6 - 0.5Simplify Equation: Simplify the equation further: 3.5h = 2.1 Now, divide both sides by 3.5 to solve for h: h = 2.1 / 3.5Calculate h Value: Calculate the value of h: h = 0.6 So, it will take Joseph 0.6 hours to catch up to Sandra.

Full solution

More problems from Solve linear equations with variables on both sides: word problems

Related topics