Solve the problem. Estimate to check your solution is reasonable.
1. During a 1 hour phone in talk show eight callers made calls hat took 3 1/4 minutes each.
a) How many minutes were used by the eight callers?
b) what fraction of the hour was used by callers?
c) how many minutes were left for other callers?
d) what fraction of the hour was left for other callers?
a. 26 minutes
b. 26/60 = ?
I'll be glad to check your answers for c and d.
To solve this problem, we can break it down step by step:
a) How many minutes were used by the eight callers?
To find the total number of minutes used by eight callers, we multiply the number of callers by the duration of each call. In this case, eight callers made calls that took 3 1/4 minutes each. To convert the mixed number (3 1/4) to an improper fraction, we multiply the whole number (3) by the denominator (4) and add the numerator (1). This gives us a total of 13/4 minutes per call. Multiplying this by 8 callers, we get:
Total minutes used = (8 callers) * (13/4 minutes per call) = 104/4 minutes = 26 minutes.
b) What fraction of the hour was used by callers?
Since the phone-in talk show lasted for 1 hour, we can express the fraction of the hour used by callers as a ratio of the minutes used by callers to the total minutes in an hour. Using the result from the previous question, we have:
Fraction of the hour used by callers = (26 minutes) / (60 minutes) = 13/30.
c) How many minutes were left for other callers?
To find the minutes left for other callers, we subtract the minutes used by the eight callers from the total minutes in an hour. So, we have:
Minutes left for other callers = (60 minutes) - (26 minutes) = 34 minutes.
d) What fraction of the hour was left for other callers?
Similar to the previous question, we express the fraction of the hour left for other callers as a ratio of minutes left for other callers to the total minutes in an hour. Using the result from the previous question, we have:
Fraction of the hour left for other callers = (34 minutes) / (60 minutes) = 17/30.
To estimate and check our solution for reasonableness, we can consider that each call took approximately 3 minutes. Since there were 8 callers in 1 hour, we would expect the total minutes used to be around 24 minutes. Our calculated answer of 26 minutes is close to our estimate, which suggests that our solution is reasonable.
Therefore, the answers to the provided questions are:
a) The eight callers used 26 minutes.
b) The fraction of the hour used by callers is 13/30.
c) There were 34 minutes left for other callers.
d) The fraction of the hour left for other callers is 17/30.