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A race car driver drives a miles in qualifying in p hours

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A race car driver drives a miles in qualifying in p hours

by M7MBA » Fri Apr 13, 2018 6:19 am

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A race car driver drives "a" miles in qualifying in "p" hours and then drives "b" miles in "2p" hours. Which of the following represents the driver's average speed, in miles per hour, for the two sets of driving?

A. (a+b)/p
B. (a+b)/(3p)
C. 3p/(b-a)
D. 2(a+b)/(3p)
E. p/(2(a-b))

The OA is B.

What are the formulas that are needed here? Any help? Thanks.
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by Sionainn@PrincetonReview » Fri Apr 13, 2018 6:38 am
To find the average speed, divide the total distance by the total time.

So algebraically, the total distance is a + b. The total time is p + 2p or 3p. So the average speed is (a +b)/3p or B.

You can also make it more concrete by plugging in numbers. Let's say a = 10, b = 30 and p = 2. Then the total distance is 10 + 30 or 40 miles and the total time is 2 + 2*2 or 6 hours. So the average speed is 40 miles/6 hours or 6 2/3 miles per hour. Then go to the answer choices replacing a = 10, b = 30 and p = 2 and see which one gives the answer of 6 2/3.

Take care,

Sionainn Marcoux
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.
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by swerve » Sat Apr 14, 2018 10:13 am
$$Dist=speed\cdot time$$
$$a=s\cdot p$$
$$b=s\cdot2p$$
Combining these two together:
$$a+b=s*p+s*2p$$
$$a+b=s(p+2p)$$
$$s=\frac{a+b}{3p}$$
Option B.

Regards!
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by Scott@TargetTestPrep » Wed Apr 25, 2018 3:48 pm
M7MBA wrote:A race car driver drives "a" miles in qualifying in "p" hours and then drives "b" miles in "2p" hours. Which of the following represents the driver's average speed, in miles per hour, for the two sets of driving?

A. (a+b)/p
B. (a+b)/(3p)
C. 3p/(b-a)
D. 2(a+b)/(3p)
E. p/(2(a-b))
We can use the formula for average rate:

average rate = total distance/total time

average rate = (a + b)/(p + 2p) = (a + b)/(3p)

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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