1. Sophia and Melody were biking together. along a straight bikeway from two positions.At one point Sophia stopped to rest, while Melody continued to bike. Sophia resumed biking again but at a faster pace of 22 miles per hour, while Melody continued at asteady pace of 15 miles per hour to allow Sophia to catch up. Sophia finally caughtup with Melody after 6 minutes. How far behind (in miles) was Sophia when she resumed biking? Please express the answer in decimal points.

2. One mile is 5280 feet, and 3 feet is one yard. A professional soccer player runs upto 7 miles in a 90-minute match. It averages to how many yards every 9 seconds?Please round the answer to the nearest yard.

3. On average customers order one pizza every 3 minutes and 20 seconds from Mathni-fient Pizza, and today (due to a mishap) they only have enough raw materials tomake 45 pizzas. They started selling pizza at 05:10pm. At what time does Math-nificent expect to sell out all pizzas?Please write the answer in the 12-hour hh:mm format. For example,9:30pm would be 09:30.

4. Linda drove 50 miles from San Jose to San Francisco in 90 minutes. For the first 30 minutes, without much traffic, her average speed was 60 miles an hour. In the second 30 minutes, due to a traffic accident along US 101, her average speed dropped to 35 miles an hour. She was stuck in traffic for the last 30 minutes near San Francisco.What was her average speed, in miles per hour, during the last 30 minutes?

Potatobird Jan 22, 2021

#1**+2 **

1. Sophia and Melody were biking together. along a straight bikeway from two positions.At one point Sophia stopped to rest, while Melody continued to bike. Sophia resumed biking again but at a faster pace of 22 miles per hour, while Melody continued at asteady pace of 15 miles per hour to allow Sophia to catch up. Sophia finally caughtup with Melody after 6 minutes. How far behind (in miles) was Sophia when she resumed biking? Please express the answer in decimal points

Notice that the difference in rates = (22 - 15) = 7 mph = Sophia's effective rate

6 min = 1/10 hr

So rate * time = distance

7 (1/10) = 7/10 = .7 miles behind

2. One mile is 5280 feet, and 3 feet is one yard. A professional soccer player runs upto 7 miles in a 90-minute match. It averages to how many yards every 9 seconds?Please round the answer to the nearest yard.

No. of yards run = 5280 / 3 * 7 = 12320 yards

90 min =1.5 hrs

No. of seconds in 1.5 hrs = 1.5 * 60 min * 60sec = 5400 sec

Yds run per second = 12320 / 5400 = 308/135 yds

Yds run in 9 sec = (308/ 135) * 9 ≈ 21 yds in 9 sec

CPhill Jan 23, 2021

#2**+2 **

3. On average customers order one pizza every 3 minutes and 20 seconds from Mathni-fient Pizza, and today (due to a mishap) they only have enough raw materials tomake 45 pizzas. They started selling pizza at 05:10pm. At what time does Math-nificent expect to sell out all pizzas?Please write the answer in the 12-hour hh:mm format. For example,9:30pm would be 09:30.

3 min + 20 sec = 3 + 1/3 min = 10/3 min for one pizza

So 45 pizzas take 45 * 10 /3 = 150 min = 2 hrs 30 min

So

5:10 PM + 2hrs 30 min = 7: 40 PM when they sell out

CPhill Jan 23, 2021

#3**+2 **

4. Linda drove 50 miles from San Jose to San Francisco in 90 minutes. For the first 30 minutes, without much traffic, her average speed was 60 miles an hour. In the second 30 minutes, due to a traffic accident along US 101, her average speed dropped to 35 miles an hour. She was stuck in traffic for the last 30 minutes near San Francisco.What was her average speed, in miles per hour, during the last 30 minutes?

Trick question.....she didn't move in the last 30 min.....avg speed during this time = 0 mph

CPhill Jan 23, 2021