1.) A consulting engineer\'s time is billed at $40 per hour, and her assistant\'

Question

1.)

A consulting engineer's time is billed at $40 per hour, and her assistant's is billed at $20 per hour. A customer received a bill for $610 for a certain job. If the assistant worked 4 hours less than the engineer, how much time did each bill on the job?
2.)

A runner starts at the beginning of a runners' path and runs at a constant rate of 5 mi/hr. Three minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course. How long will it take the second runner to reach the first?

3.)

In a certain medical test designed to measure carbohydrate tolerance, an adult drinks 6 ounces of a 80% glucose solution. When the test is administered to a child, the glucose concentration must be decreased to 60%. How much 80% glucose solution and how much water should be used to prepare 6 ounces of 60% glucose solution?

Explanation / Answer

a) let engineer worked for x hours

then assistant worked for x - 4 hours

engineer cost is $ 40 per hour

assistant cost is $ 20 per hour

for x hours it would be

x * 40 + (x-4) * 20 = 610

40x + 20x - 80 = 610

60 x = 690

x = 11.5

engineer worked for 11.5 hours approximately and assistant worked for 11.5 - 4 = 7.5 hours

2) first runner rate = 5mi/hr

3 minutes later 2nd runner rate = 8mi/hr

let time be t

distance covered by first runner = 5*t

distance covered by 2nd runner = 8 ( t-.05)

equating the two distances

5t = 8(t-.05)

5t = 8t - .4

-3t = -.4

t = -.4 / -3 = .1333

hence after .1333*60 = 8 minutes second runner will reach to first runner

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