A travel agent is trying to schedule a client's trip from City A to City B . There are 3 direct flights,3 flights from A to a connecting city C , and 4 flights from this connecting City C to City B .How many trips are possible?
possible number of routes by connecting city = (3)(4) = 12
also 3 direct flights, so a total of 15
Well, let me put on my travel agent hat and do some calculations here. If there are 3 direct flights from City A to City B, and 3 flights from A to a connecting city C, that means there are a total of 6 different routes from City A to City C. Now, if there are 4 flights from city C to City B, that gives us a grand total of 24 possible routes from City A to City B. So, pack your bags and get ready for some serious flight options!
To determine the number of possible trips, we need to consider each leg of the journey separately.
First, let's consider the direct flights from City A to City B. Since there are 3 direct flights, there are 3 possible trips.
Next, let's consider the flights from City A to a connecting city C. Since there are 3 flights from A to C, for each direct flight, there are 3 possible trips from City A to City C.
Finally, let's consider the flights from the connecting City C to City B. Since there are 4 flights from C to B, for each trip from City A to City C, there are 4 possible trips from City C to City B.
Therefore, the total number of possible trips is calculated by multiplying the number of direct flights, flights from A to C, and flights from C to B:
3 (direct flights) * 3 (flights from A to C) * 4 (flights from C to B) = 36 possible trips.
So, there are 36 possible trips from City A to City B considering the given flights.
To determine the number of possible trips, we need to consider the different combinations of direct and connecting flights.
1. Direct Flights: Since there are 3 direct flights from City A to City B, the client can choose any one of these flights.
2. Connecting Flights:
a. From City A to connecting City C: There are 3 flights available.
b. From connecting City C to City B: There are 4 flights available.
To calculate the total number of possible trips, we need to multiply the number of choices in each category:
Total number of trips = Number of direct flights * Number of flights from A to C * Number of flights from C to B
Total number of trips = 3 * 3 * 4 = 36
Therefore, there are 36 possible trips for the client from City A to City B, considering both direct and connecting flights.