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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?

Ask by Mckenzie Cruz. in the United States
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The two buses will be 400 miles apart at 8:00 PM.

Solution

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**.

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The Deep Dive

To solve this problem, we can use the formula: distance = speed × time. Let’s denote the time they travel until they are 400 miles apart as "t" hours. Since the buses are traveling in opposite directions, we can add their distances together: Distance covered by the first bus = 55t, Distance covered by the second bus = 45t. Together, the total distance between the two buses will be: 55t + 45t = 100t. We want this total distance to equal 400 miles, so we set up the equation: 100t = 400. Solving for t, we divide both sides by 100: t = 4 hours. So, they will be 400 miles apart at 8 pm local time! Now, just imagine the two drivers cranking up their favorite tunes, racing against the clock, and spreading their travel stories to friends while zooming down the highway. Everyone is happy when you keep the wheels rolling!

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