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For every mile of highway on land, the city needs two truckloads of asphalt and one gallon of paint. For every mile of highway on bridges, the city needs one truckload of asphalt and three gallons of paint. The city has 50 truckloads of asphalt and 80 gallons of paint.

(a) What is the largest total number of miles of highway the city can build?

(b) Suppose the city is on an island and must build at least 25 miles of highway on bridges to reach other islands. Now what is the largest total number of miles of higway the city can build?

 Jul 5, 2020
 #1
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A   Are they are limited to the amount of paint they have?      80g / 1 g/mile  = 80 miles       using all of the paint

          50 trucks /2 trucks/mile  = 25 miles     using all of the  trucks of asphalt

 

B    25 miles of bridge =  =    25 trucks   leaving 25 trucks of asphalt         25 trucks/2 trucks/mile = 12.5 miles of land highway  possible

       25 miles of bridge =       25 miles x 3 gal/mile = 75 gallons of paint    leaving only 5 gallons of paint for 5 add'l land miles

          25 miles of bridge + 5 land miles = 30 miles total highway .

 Jul 5, 2020

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