Question

HELP!!!

Xavier rides his motorcycle to pick up Olivia and they ride back to Xavier’s house together on the motorcycle. The average speed s for the 5-mile trip to Olivia’s house is 2 miles per hour faster when he rides alone. What is an expression for the total travel time? If he rides 30 mph to Olivia’s house, how long does the entire trip take?

Answer 1

The total round trip time for Xavier to pick up Olivia and return is approximately 20.76 minutes, assuming the speed to Olivia's house is 30 mph and it is 2 mph slower on the way back.

Step-by-step explanation:

To calculate the expression for the total travel time for the round trip, we need to account for the speed difference when Xavier travels alone versus when he's with Olivia. If the average speed when Xavier rides alone to Olivia's house is 30 mph, and it's 2 mph less on the way back, we have:

Speed to Olivia's house: 30 mph

Speed back to Xavier's house: 30 mph - 2 mph = 28 mph

The distance to and from Olivia's house is 5 miles each way. To find the time for each leg of the trip, we use the formula time = distance / speed.

Time to Olivia's house: time = 5 miles / 30 mph = 1/6 hours

Time back to Xavier's house: time = 5 miles / 28 mph ≈ 0.179 hours

Add the times together for the total travel time:

Total travel time ≈ 1/6 hours + 0.179 hours ≈ 0.346 hours.

To convert this to minutes, multiply by 60:

Total travel time in minutes ≈ 0.346 hours x 60 ≈ 20.76 minutes.

Therefore, the entire round trip takes approximately 20.76 minutes.

Answer 2

The expression for the total travel time is t + t_2, where t is the time taken for Xavier to ride to Olivia's house and t_2 is the time taken for them to ride back together. If Xavier rides at a speed of 30 mph to Olivia's house, the total travel time can be calculated by substituting the given values into the expression.

Step-by-step explanation:

The total travel time can be expressed as the sum of the time it takes for Xavier to ride to Olivia's house and the time it takes for them to ride back to Xavier's house together. Let's denote the time it takes for Xavier to ride to Olivia's house as t. Since the average speed is 2 mph faster when he rides alone, his speed when riding alone would be 30 mph - 2 mph = 28 mph. The distance to Olivia's house is 5 miles, so the time taken would be t = d/s = 5 miles / 28 mph.

The time it takes for Xavier and Olivia to ride back together can be calculated using the average speed, denoted as s_2. Given that the average speed is 2 mph faster when he rides alone, we can write s_2 = 30 mph = 28 mph + 2 mph. The distance from Olivia's house back to Xavier's house is also 5 miles. Therefore, the time taken for this leg of the trip would be t_2 = d_2 / s_2 = 5 miles / 30 mph.

The total travel time can be expressed as the sum of the individual travel times: total travel time = t + t_2. Substituting the values we calculated earlier, we get total travel time = 5 miles / 28 mph + 5 miles / 30 mph. To calculate the actual value of the total travel time, we can substitute the given speed of 30 mph for the second leg of the trip and perform the calculations.