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?
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The instructions given makes the question more complicated than it has to be ...
time for the regular bus is t hrs
time for the express is t-1 hrs
distance covered by regular bus = 40t miles
distance covered by express bus = 50(t-1) miles
so:
50(t-1) = 40t
50t-50 = 40t
t = 5
the regular bus went for 5 hrs and the express bus went for 4 hours when they met, each having covered 200 miles.
(the 220 distance had nothing to do with the solution, it simply assured that they met before the journey was completed)
To answer these questions, let's break down the problem step by step.
A. To find the sum of the distances the buses have traveled when they meet, we'll need to calculate the distance traveled by each bus. The first bus travels at a speed of 40 miles per hour for a total of t hours, where t is the time taken by the express bus until they meet. Hence, the distance traveled by the first bus is 40t miles. The express bus, on the other hand, travels at a speed of 50 miles per hour for one hour less than the first bus. So, the distance traveled by the express bus is 50(t-1) miles. The sum of these distances is 40t + 50(t-1).
B. To represent the travel time of the other bus, we need to find the time it took for the first bus to reach the meeting point. As given in the problem, the express bus left one hour later than the first bus. So, the express bus's travel time can be represented as t-1 hours.
C. Using the formula distance = rate x time, we can create an equation 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. The equation becomes:
40t + 50(t-1) = 220.
D. Now, we can solve the equation to find the time when the buses meet. Simplifying the equation:
40t + 50t - 50 = 220,
90t - 50 = 220,
90t = 270,
t = 3.
Therefore, the buses meet after 3 hours. The express bus started one hour later than the first bus, so it took 3-1 = 2 hours for the express bus to reach the meeting point. The first bus left Trawlwy at 9:00am, so the buses pass each other at 9:00am + 2 hours = 11:00am.