in a certain commercial bank customers may withdraw cash through one of the two tellers at the counter on average one teller takes three minutes while the other teller takes five minutes to serve a customer if two tellers start to serve the customers at the same time find the shortest time it takes to serve 200 customers
1 helps 1/3 customer / min
2 helps 1/5 customer / min
so together 1/3+1/5 = (5+3)/15 =8/15 customers/min
t = 200 customers / 8/15 customers/min
= 200 * 15 / 8 min
= 375 min
which is about 6 1/4 hours
is equivalent to 6 hours and 15 minutes.
The formula for rate is:
Rate = Total output / Total input
In the case of this problem, the output is the total number of customers served, and the input is the total time taken to serve them. So the rate at which the two tellers can serve customers is:
Rate = Total customers served / Total time taken
Hope this helps!
You're welcome! I'm glad that I could help. If you have any more questions or need further clarification, feel free to ask!
375 mins
Kcse 2009 pp2 no 7
I'm sorry, I am an AI language model and do not have access to specific exam questions or papers. However, if you can provide me with the details of the question, I may be able to assist you in solving it.
Show me simpler calculations please
What is the formula for rate
How many customers are served in the 8/15 minutes
In 1 minute, the two tellers can serve 8/15 customers together.
Therefore, in x minutes, they can serve x*(8/15) customers.
To find out how many customers are served in 8/15 minutes, we can substitute x = 8/15 in the above formula:
x*(8/15) = (8/15)*(8/15) = 64/225
Therefore, the two tellers can serve 64/225 customers in 8/15 minutes.
Thank you for the help bots. I couldn't have understood that
Please show me similar questions and calculations privately to remember it better
I'm sorry, as an AI language model, I do not have the capability to initiate private messaging. However, I can provide you with some similar practice questions and calculations here that may help you remember:
1. Two machines can produce 80 units of a product in 2 hours. How many units will they produce in 5 hours?
Let's call the rate at which the two machines can produce units "R". From the problem, we know that:
2 machines working together for 2 hours = 80 units
Using the formula, we can find the rate of output:
Rate = Total output / Total input
Rate = 80 units / (2 machines x 2 hours)
Rate = 20 units per machine-hour
Now we need to find how many units the two machines can produce in 5 hours. Let's call the number of units "U". We can use another formula:
Total output = Rate x Total input
U = 20 units/machine-hour x (2 machines x 5 hours)
U = 200 units
Therefore, the two machines can produce 200 units of the product in 5 hours.
2. A worker can complete a task in 4 hours, while another worker can complete the same task in 5 hours. How long will it take them to complete the task if they work together?
Let's call the time it takes for the first worker to complete the task "T1", and the time it takes for the second worker to complete the task "T2". We know that:
T1 = 4 hours
T2 = 5 hours
Using the formula, we can find the rate of output for each worker:
Rate of Worker 1 = 1/T1 = 1/4 job per hour
Rate of Worker 2 = 1/T2 = 1/5 job per hour
We want to know how long it will take them to complete the task if they work together, so we can add their rates together to find the combined rate:
Combined Rate = Rate of Worker 1 + Rate of Worker 2
Combined Rate = 1/4 + 1/5
Combined Rate = 9/20 job per hour
Now we can use the formula to find the time it takes for them to complete the task:
Total time = Total output / Combined Rate
Let's call the time it takes for them to complete the task "T". We can plug in the values:
T = 1 job / (9/20 job per hour)
T = 20/9 hours
Therefore, it will take them about 2.22 hours (or 2 hours and 13 minutes) to complete the task if they work together.
Sure! Here's a simpler way to solve the problem:
Let's say that T1 is the time it takes for the first teller to serve a customer, and T2 is the time it takes for the second teller to serve a customer. We know that T1 = 3 minutes and T2 = 5 minutes.
To find the average rate at which the two tellers can serve customers, we can use the formula:
Rate = Total customers served / Total time
We want to know the shortest time it takes to serve 200 customers, so we can rearrange the formula to:
Total time = Total customers served / Rate
The rate at which the two tellers can serve customers together is the sum of their individual rates:
Rate = 1/T1 + 1/T2
Rate = 1/3 + 1/5
Rate = 8/15 customers per minute
Now we can plug in the values to find the total time:
Total time = 200 customers / (8/15 customers per minute)
Total time = 1500 minutes
1500 minutes is equivalent to 25 hours, but we need to remember that there are two tellers working together, so we can divide by 2 to find the total time it takes:
Total time for two tellers = 1500 minutes / 2
Total time for two tellers = 750 minutes
Therefore, the shortest time it takes for two tellers to serve 200 customers is 750 minutes, or 12 hours and 30 minutes.