Question

Two bakers make 30 loaves of bread every morning. Assume all bakers work at the same rate. Suppose two bakers make 30 loaves in one hour. How many hours would 3, 5, 6, and 15 bakers need to make 30 loaves?

Answer 1

Explanation:

2 bakers make 30 loaves in 1 hour.

that means each baker just by him-/herself can make 15 loaves in 1 hour.

so,

1 baker's "speed" = 15 loaves/hr

15 l/h = 30l/x

x = 30/15 = 2 hours (1 baker takes 2 hours to make 30).

3 bakers' speed = 3×15/hr = 45l/h

45l/h = 30l/x

x = 30/45 = 2/3 hours (3 bakers need 2/3 hours = 40 minutes to make 30 loaves).

5 bakers = 5×15l/h = 75 l/h.

75l/h = 30l/x

x = 30/75 = 2/5 hours (5 bakers need 2/5 hours = 2×60/5 = 24 minutes to make 30 loaves).

6 bakers = 6×15l/h = 90 l/h.

90 l/h = 30/x

x = 30/90 = 1/3 hours (6 bakers need 1/3 hour = 60/3 = 20 minutes to make 30 loaves).

15 bakers = 15×15 l/h = 225 l/h

225 l/h = 30/x

x = 30/225 = 2/15 hours (15 bakers need 2/15 hours = 2×60/15 = 2×4 = 8 minutes to make 30 loaves).

Answer 2

We can use the formula:

time = (amount of work) / (rate of work)

The rate of work is the number of loaves made per hour by one baker. Since two bakers can make 30 loaves in one hour, the rate of work is:

rate of work = (30 loaves) / (2 bakers) = 15 loaves per baker per hour

Now we can use this rate to find how long it takes different numbers of bakers to make 30 loaves:

- For 3 bakers: time = (30 loaves) / (3 bakers x 15 loaves per baker per hour) = 0.67 hours, or about 40 minutes.
- For 5 bakers: time = (30 loaves) / (5 bakers x 15 loaves per baker per hour) = 0.4 hours, or 24 minutes.
- For 6 bakers: time = (30 loaves) / (6 bakers x 15 loaves per baker per hour) = 0.33 hours, or 20 minutes.
- For 15 bakers: time = (30 loaves) / (15 bakers x 15 loaves per baker per hour) = 0.133 hours, or 8 minutes.