Question

math antics worksheets date: using unit rates to compare instructions: use unit rates to solve the following word problems. 1 tom and paul are building a brick wall. tom lays 420 bricks in 6 hours. paul lays 240 bricks in 3 hours. whose rate is faster? tom’s rate \\(\frac{420}{6} = \frac{70}{1}\\) bricks per hour paul’s rate \\(\frac{240}{3} = \frac{80}{1}\\) bricks per hour \\(70 < 80\\) so paul’s rate is faster. 31 kim and ben are planting a garden. kim plants 24 flowers in 2 hours. ben plants 33 flowers in 3 hours. whose rate is faster? 32 ann’s bakery bakes 450 loaves of bread in 3 days. mark’s bakery bakes 560 loaves of bread in 4 days. which bakery bakes bread at the faster rate? 33 dave and eric are painting a long fence. dave paints 125 feet of the fence in 5 hours. eric paints 175 feet in 7 hours. whose rate is faster? 34 a bear can run 400 feet in 8 seconds. a horse can run 290 feet in 5 seconds? which animal runs at the faster rate? 35 sam earned $380 working for 8 hours. rich earned $195 working for 4 hours. who has the higher rate of pay? 35. \\(\square\\) rate is higher because \\(\square < \square\\) show your work

Explanation:

Problem 31: Kim and Ben Planting Flowers

Step1: Calculate Kim's rate

Kim plants 24 flowers in 2 hours. To find the unit rate (flowers per hour), divide the number of flowers by the number of hours.
$\frac{24}{2} = 12$ flowers per hour.

Step2: Calculate Ben's rate

Ben plants 33 flowers in 3 hours. Divide the number of flowers by the number of hours.
$\frac{33}{3} = 11$ flowers per hour.

Step3: Compare the rates

Compare 12 and 11. Since $11 < 12$, Kim's rate is faster.

Step1: Calculate Ann's Bakery rate

Ann's Bakery bakes 450 loaves in 3 days. Unit rate (loaves per day) is $\frac{450}{3} = 150$ loaves per day.

Step2: Calculate Mark's Bakery rate

Mark's Bakery bakes 560 loaves in 4 days. Unit rate is $\frac{560}{4} = 140$ loaves per day.

Step3: Compare the rates

Since $140 < 150$, Ann's Bakery has a faster rate.

Step1: Calculate Dave's rate

Dave paints 125 feet in 5 hours. Unit rate (feet per hour) is $\frac{125}{5} = 25$ feet per hour.

Step2: Calculate Eric's rate

Eric paints 175 feet in 7 hours. Unit rate is $\frac{175}{7} = 25$ feet per hour.

Step3: Compare the rates

Both have a rate of 25 feet per hour, so their rates are equal.

Answer:

Kim's rate is higher because $11 < 12$.

Problem 32: Ann's and Mark's Bakeries