A bus leaves a station at 8:00 am and averages 30 mi/h. Another bus leaves the same station following the same route two hours after the first and averages 50 mi/h. When will the second bus catch up with the first bus?
in the two hours between the buses, the first bus has traveled 60 miles.
So, the other bus must make up 60 miles at 50 mi/hr, which will take 60/50 hours.
Add that time to the bus's departure time.
In 5 days
12 pm
50 time 30 is 150
8 30
9 60
10. 90. 50
11. 120. 100
12. 150. 150
To determine when the second bus will catch up with the first bus, we need to find the time it takes for the two buses to travel the same distance.
Let's break down the problem step by step:
1. We know that the first bus leaves at 8:00 am and travels at an average speed of 30 mi/h.
2. The second bus leaves two hours later, which means it starts its journey at 10:00 am. The second bus travels at an average speed of 50 mi/h.
3. Since the two buses are traveling on the same route, we can consider the distance between them to be constant. Let's call this distance "D".
4. To find the time it takes for the second bus to catch up with the first bus, we can set up an equation based on the distance, speed, and time relationships.
Let's denote the time it takes for the second bus to catch up with the first bus as "t" hours. Here's the equation we can create:
Distance traveled by the first bus = Distance traveled by the second bus
30t = 50(t - 2)
The first part of the equation (30t) represents the distance traveled by the first bus, which has been traveling for "t" hours at a speed of 30 mi/h.
The second part of the equation (50(t - 2)) represents the distance traveled by the second bus. Since the second bus leaves two hours later, it has been traveling for "(t - 2)" hours at a speed of 50 mi/h.
Now, we can solve this equation to find the value of "t" when the second bus catches up with the first bus.
30t = 50(t - 2)
30t = 50t - 100
100 - 30t = 50t
100 = 80t
t = 100/80
t = 1.25
Therefore, it will take 1.25 hours (or 1 hour and 15 minutes) for the second bus to catch up with the first bus. To find the exact time when this happens, we need to add this time to the departure time of the second bus (10:00 am). Therefore, the second bus will catch up with the first bus at 11:15 am.