The bus stations in Trawlwy and Fenton are 220 miles apart. A bus left Trawley for Fenton at 9:00am. Traveling at 40 miles per hour. One hour later, an express bus left Fenton for Trawley traveling along the same road at 50 miles per hour. At what time did the buses pass each other?
A. When the buses meet, what is the sum of the distances they have travelled?
B. Let t represent the time the express bus was traveling when they met. What expression represents the travel time of the other bus?
C. Use the formula distance = rate x time. What equation models the situation?
D. Solve the equation. At what time did the buses meet?
A. 220 Miles.
B. 40(t+1).
C. 40(t+1) + 50t = 220
D. 40t + 40 + 50t = 220
90t = 220-40 = 180
t = 180/90 = 2 hrs.
T=9:00AM + (t+1)=9:00 + 3 hrs=12 Noon.
= The time they met.
A. To find the sum of the distances the buses have traveled when they meet, we need to consider the distance each bus has covered. The first bus has been traveling for t hours (since it left one hour earlier), so its distance traveled is 40t miles. The second bus has been traveling for (t - 1) hours, as it left one hour later than the first bus. Therefore, the distance it traveled is 50(t - 1) miles. The sum of these distances is 40t + 50(t - 1) miles.
B. Let's represent the travel time of the other bus, which is the first bus in this case, as t. This means that the express bus has been traveling for (t - 1) hours, as it left one hour later.
C. The formula distance = rate x time can be used to model the situation. The distance traveled by the first bus is 40t miles, and the distance traveled by the express bus is 50(t - 1) miles. Therefore, the equation representing the situation is 40t + 50(t - 1) = 220.
D. To solve the equation, we can begin by simplifying it. Distributing the 50 to t and -1 gives us 40t + 50t - 50 = 220. Combining like terms, we have 90t - 50 = 220. Adding 50 to both sides, we get 90t = 270. Dividing both sides by 90, we find that t = 3.
Therefore, the buses meet after 3 hours. Since the first bus left at 9:00am, they meet at 9:00am + 3 hours = 12:00pm.