21. Two buses leave Houston et 4 pm local time and travel in opposite dircetions. One bus averages 55 mph . and the other bus averages 45 mph . At what tume will they be 400 miles apan?

To determine **at what time** the two buses will be **400 miles apart**, let's break down the problem step by step. ### **Given:** - **Start Time:** 4:00 PM - **Bus A Speed:** 55 mph - **Bus B Speed:** 45 mph - **Total Distance Apart:** 400 miles ### **Understanding the Movement:** - Since both buses are traveling in **opposite directions**, their speeds **add up** when calculating the rate at which the distance between them increases. ### **Calculating the Relative Speed:** \[ \text{Combined Speed} = \text{Speed of Bus A} + \text{Speed of Bus B} = 55\ \text{mph} + 45\ \text{mph} = 100\ \text{mph} \] ### **Determining the Time to Reach 400 Miles Apart:** \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{400\ \text{miles}}{100\ \text{mph}} = 4\ \text{hours} \] ### **Final Calculation:** - **Start Time:** 4:00 PM - **Time Taken:** 4 hours - **Final Time:** 4:00 PM + 4 hours = **8:00 PM** ### **Conclusion:** The two buses will be **400 miles apart at 8:00 PM**.