Determine the color, driver and mpg of each car by the information:
* Five different drivers -- Cox, Durham,Gosling, Heynek and Wollinsky.
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* Car colors-- blue, green, red, white and yellow.
---------------------------------------* Each had different mpg-- 32, 31, 30, 29 and 28
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1. Durham got more mpg than the green car but not as many as the red car.
2. The blue car got better mpg than the car driven by Wollinsky
3. Cox did not drive the green or red car
4. The yellow car got more mpg than the car driven by Gosling but not as many as the green car.
Determine driver, color and mpg of each car.
make some index cards for each driver, and car.
Line the cards up, two rows, one row for cars, one row for drivers. You will match them soon enough.
To determine the driver, color, and mpg of each car, we can use a logic grid to organize the given information.
First, let's create a grid with the drivers, colors, and mpg as the rows and columns:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | | | | |
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MPG | | | | |
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Now, let's fill in the given information:
1. Durham got more mpg than the green car but not as many as the red car.
From this information, we can deduce that Durham did not drive the green or red car.
So, let's fill in the grid accordingly:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | | | | |
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MPG | | | | |
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2. The blue car got better mpg than the car driven by Wollinsky.
This means that the blue car must have more mpg than the car driven by Wollinsky.
So, let's fill in the grid accordingly:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | | | | |
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MPG | | | | |
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3. Cox did not drive the green or red car.
From this information, we can deduce that Cox drove either the blue, white, or yellow car.
So, let's fill in the grid accordingly:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | | | | |
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MPG | | | | |
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4. The yellow car got more mpg than the car driven by Gosling but not as many as the green car.
From this information, we can deduce that the green car must have more mpg than the yellow car, and the yellow car must have more mpg than the car driven by Gosling.
So, let's fill in the grid accordingly:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | | | | |
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MPG | | | | |
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Now, let's analyze the remaining information to complete the grid:
- There are five different drivers, so each row in the driver column should have a unique value.
- There are five different colors, so each row in the color column should have a unique value.
- There are five different mpg values, so each row in the mpg column should have a unique value.
Let's look at the remaining driver column:
| Cox | Durham | Gosling | Heynek | Wollinsky
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| | | |
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We still need to assign drivers to the blue, white, and yellow cars. Cox cannot drive the red or green car, so Cox must drive the blue car.
| Cox | Durham | Gosling | Heynek | Wollinsky
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| Blue | | |
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Now let's fill in the remaining columns:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | | | |
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MPG | | | | |
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The blue car got better mpg than the car driven by Wollinsky, so Wollinsky cannot drive the blue car. The remaining drivers who can drive the blue car are Durham, Gosling, and Heynek. Durham gets more mpg than the green car but not as many as the red car, so Durham cannot drive the blue or green car. Therefore, the remaining options are Gosling and Heynek.
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | | | |
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MPG | | | | |
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Cox did not drive the green or red car, so the green and red cars are assigned to Durham and Wollinsky.
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | Red | ? | ? | Green
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MPG | | | | |
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Finally, the yellow car got more mpg than the car driven by Gosling but not as many as the green car. Since Durham has the red car, the remaining options for Gowling are yellow and white. However, the yellow car gets more mpg than the car driven by Gosling, so Gosling must drive the white car. This means that Heynek drives the yellow car.
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | Red | White | Yellow | Green
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MPG | | | | |
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The remaining car color options for Durham are blue and white. However, the blue car gets better mpg than the car driven by Wollinsky, so Wollinsky must drive the white car. This means that Durham drives the blue car.
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | Red | White | Yellow | Green
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MPG | | | | |
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Now, we only have two drivers left - Cox and Heynek. Cox cannot drive the green or red car, so he must drive the yellow car. This means that Heynek drives the green car.
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | Red | White | Yellow | Green
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MPG | | | | |
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Finally, we assign the remaining mpg values:
| Cox | Durham | Gosling | Heynek | Wollinsky
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Color | Blue | Red | White | Yellow | Green
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MPG | 30 | 29 | 28 | 31 | 32
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Therefore, the driver, color, and mpg of each car are as follows:
- The blue car is driven by Cox and has an mpg of 30.
- The red car is driven by Durham and has an mpg of 29.
- The white car is driven by Wollinsky and has an mpg of 28.
- The yellow car is driven by Gosling and has an mpg of 31.
- The green car is driven by Heynek and has an mpg of 32.