Question

6 (11) On a map drawn to scale, $\frac{1}{3}$ inch = 60 miles. (a) (5 points) How many miles is equal to one inch? (b) (5 points) On the same map, the distance between Belmont and Smithville is 13.25 inches. How long it will take to drive from Belmont to Smithville at an average speed of 60 miles per hour? Recall that distance = speed \times travel time. Please show all your computation works. (12) A machine for producing choco-nuts gives 5 choco-nut hearts for every 4 chocolate bars and $1 \frac{1}{2}$ cup of nuts put into the machine (nothing is lost in the machine). Solve by reasoning and calculating. (a) (3 points) How many hearts (might be partial) would the machine give for 18 bars and the right amount of nuts? (b) (3 points) How many cups of nuts would be the right amount for 18 bars? (c) (3 points) An order for 48 hearts comes in. How many bars will that order take?

          6
(11) On a map drawn to scale, $\frac{1}{3}$ inch = 60 miles.
(a) (5 points) How many miles is equal to one inch?
(b) (5 points) On the same map, the distance between Belmont and Smithville is
13.25 inches. How long it will take to drive from Belmont to Smithville at an
average speed of 60 miles per hour? Recall that distance = speed \times travel time.
Please show all your computation works.
(12) A machine for producing choco-nuts gives 5 choco-nut hearts for every 4 chocolate
bars and $1 \frac{1}{2}$ cup of nuts put into the machine (nothing is lost in the machine). Solve
by reasoning and calculating.
(a) (3 points) How many hearts (might be partial) would the machine give for 18
bars and the right amount of nuts?
(b) (3 points) How many cups of nuts would be the right amount for 18 bars?
(c) (3 points) An order for 48 hearts comes in. How many bars will that order take?

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6
(11) On a map drawn to scale, (1)/(3) inch = 60 miles.
(a) (5 points) How many miles is equal to one inch?
(b) (5 points) On the same map, the distance between Belmont and Smithville is
13.25 inches. How long it will take to drive from Belmont to Smithville at an
average speed of 60 miles per hour? Recall that distance = speed ×travel time.
Please show all your computation works.
(12) A machine for producing choco-nuts gives 5 choco-nut hearts for every 4 chocolate
bars and 1 (1)/(2) cup of nuts put into the machine (nothing is lost in the machine). Solve
by reasoning and calculating.
(a) (3 points) How many hearts (might be partial) would the machine give for 18
bars and the right amount of nuts?
(b) (3 points) How many cups of nuts would be the right amount for 18 bars?
(c) (3 points) An order for 48 hearts comes in. How many bars will that order take?

Added by Juan Manuel S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Bailey Cooper

08/15/2022

Step 1

Step 1: Since $\frac{1}{3}$ inch = 60 miles, then 1 inch = 3 $\times$ 60 miles = 180 miles. Show more…

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(11) On a map drawn to scale, $\frac{1}{3}$ inch = 60 miles. (a) (5 points) How many miles is equal to one inch? (b) (5 points) On the same map, the distance between Belmont and Smithville is 13.25 inches. How long it will take to drive from Belmont to Smithville at an average speed of 60 miles per hour? Recall that distance = speed $\times$ travel time. Please show all your computation works. (12) A machine for producing choco-nuts gives 5 choco-nut hearts for every 4 chocolate bars and $\frac{1}{2}$ a cup of nuts put into the machine (nothing is lost in the machine). Solve by reasoning and calculating. (a) (3 points) How many hearts (might be partial) would the machine give for 18 bars and the right amount of nuts? (b) (3 points) How many cups of nuts would be the right amount for 18 bars? (c) (3 points) An order for 48 hearts comes in. How many bars will that order take?

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Transcript

00:01 All right.

00:02 So it looks like we have a few different kind of unit questions, unit rate questions.

00:09 Our first one says on a math, 1 .25 inches represents 10 miles.

00:18 How far represents if two cities are six inches apart, how many miles is that in real life? so the first thing we're going to want to figure out for this is how many miles are in one inch, because 1 .25 is kind of a weird unit to work with.

00:38 So in order to find out how many miles per inch we have, we can divide 10 miles by 1 .25 inches, and we're going to get 8 miles per inch.

00:55 So 8 miles for 1 inch.

00:58 Once we have that, we can then multiply this by the six inches between our two cities.

01:06 You can see that our units are going to really nicely cancel out here, and we're going to be just left with 48 miles.

01:16 If there are six inches between two cities, that means there are 48 miles between them in real life.

01:23 Our second question has somebody who runs a marathon and runs different stretches of that marathon and different stretches of that marathon and different times and we're asked what the average speed in miles per minute is.

01:38 So again, what we're going to need to do for this is set up a ratio of miles per minutes.

01:48 And basically, in order to find an average, we're going to need the total miles over the total number of minutes.

01:57 Let me move.

02:02 One second to move this...

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