The Johnson family is planning a summer road trip to meet up with some friends who live 730 miles away from them. The family takes a scenic route through the winding roads of the countryside. They expect to complete the road in trip in three days. The distances and average speeds for the first two days of the trip are shown. Day 1: 5 hours at an average speed of 45 miles per hour Day 2: 8 hours at an average speed of 35 miles per hour The average speed on the third day is 45 miles per hour. Write an equation using letters and numbers to determine how many more hours it will take the Johnson family to reach their destination. Explain your reasoning.

Question

The Johnson family is planning a summer road trip to meet up with some friends who live 730 miles away from them. The family takes a scenic route through the winding roads of the countryside. They expect to complete the road in trip in three days. The distances and average speeds for the first two days of the trip are shown.  Day 1: 5 hours at an average speed of 45 miles per hour Day 2: 8 hours at an average speed of 35 miles per hour  The average speed on the third day is 45 miles per hour. Write an equation using letters and numbers to determine how many more hours it will take the Johnson family to reach their destination. Explain your reasoning.

Bytelearn · Accepted Answer

Define Variables and Values: Let's define the variables and the known values. We know the total distance of the trip is 730 miles. On Day 1, the family travels for 5 hours at an average speed of 45 miles per hour. On Day 2, they travel for 8 hours at an average speed of 35 miles per hour. We need to find the time (let's call it 't' hours) they will travel on Day 3 at an average speed of 45 miles per hour to complete the remaining distance.Calculate Day 1 Distance: First, we calculate the distance covered on Day 1 by multiplying the time traveled by the average speed: Distance = Time × Speed. So, for Day 1, the distance is 5 hours × 45 miles per hour.Calculate Day 2 Distance: Performing the calculation for Day 1: 5 hours × 45 miles per hour = 225 miles.Add Day 1 and Day 2 Distances: Next, we calculate the distance covered on Day 2 using the same formula: Distance = Time × Speed. For Day 2, the distance is 8 hours × 35 miles per hour.Find Remaining Distance: Performing the calculation for Day 2: 8 hours × 35 miles per hour = 280 miles.Set Up Equation for Day 3: Now, we add the distances from Day 1 and Day 2 to find the total distance covered in the first two days: 225 miles + 280 miles.Solve for Time 't': Adding the distances gives us a total of 225 miles + 280 miles = 505 miles covered in the first two days.To find the remaining distance to be covered on Day 3, we subtract the total distance covered in the first two days from the total trip distance: 730 miles - 505 miles.Performing the subtraction gives us the remaining distance: 730 miles - 505 miles = 225 miles to be covered on Day 3.Now we can set up the equation to find the time 't' it will take to cover the remaining 225 miles on Day 3 at an average speed of 45 miles per hour. The equation is: Distance = Speed × Time, or 225 miles = 45 miles per hour × t.To solve for 't', we divide both sides of the equation by 45 miles per hour: t = 225 miles / 45 miles per hour.Performing the division gives us the time 't': t = 225 miles / 45 miles per hour = 5 hours.We have found that it will take the Johnson family 5 more hours to reach their destination on the third day at an average speed of 45 miles per hour.

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