7. Bill took a trip to see a friend. His friend lives 225 miles away. He drove in town at an average of 30mph, then he drove on the interstate at an average of 70 mph. The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

Question

Mathematics

Kayleigh Ballard

Today, 06:59

7. Bill took a trip to see a friend. His friend lives 225 miles away. He drove in town at an average of 30mph, then he drove on the interstate at an average of 70 mph. The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

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Answers (1)

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Dayami Stevens · Answer 1

Bill drove 210 miles on the interstate.

Step-by-step explanation:

The total distance of his travel was 225 miles and there were two types of road in the course, the town roads at which he drove "x" miles and the interestate road at which he drove "y" miles. Therefore:

x + y = 225

On the town he drove at 30 mph on average and on the interestate he drove at 70 mph on average. Therefore:

x/30 + y/70 = 3.5

We can now build a system of equations shown below:

x + y = 225

x/30 + y/70 = 3.5

Multiplying second equation by - 30, we have:

x + y = 225

-x - (3/7) * y = - 105

(4/7) * y = 120

y = 120 * (7/4) = 210

x + 210 = 225

x = 225 - 210 = 15

Bill drove 210 miles on the interstate.