SAT Mc Graw Hill 2011

CHAPTER 9 / SPECIAL MATH PROBLEMS 349

Concept Review 4

1. Speed =#miles ÷#hours


2. Efficiency =#miles ÷#gallons


3. Typing speed =#pages ÷#minutes
   4. 375 miles ÷75 mph =5 hours for the trip.
   5. 28 miles per gallon ×4.5 gallons =126 miles the
   car can go before it runs out of fuel.
   6. 600 words ÷5 minutes =120 words per minute is
   Harold’s typing speed.
   7. 8 acres ÷1.6 acres per hour =5 hours for the job.
   8. 90 miles ÷50 mph =1.8 hours, or 1 hour 48 min-
   utes for the entire trip. At 1 hour and 48 minutes
   after 1:00 pm, it is 2:48 pm.
   9. Anne can paint one room in 2 hours, so her rate is

(^1) ⁄ 2 room per hour. Barbara can paint one room in
3 hours, so her rate is^1 ⁄ 3 room per hour. When they
work together, their rate is^1 ⁄ 2 +^1 ⁄ 3 =^5 ⁄ 6 room per hour.
So to paint one room would take one room ÷^5 ⁄ 6
room per hour =^6 ⁄ 5 hours, or 1.2 hours, or 1 hour
12 minutes.
Answer Key 4: Rate Problems
SAT Practice 4

1. 30 Working together, they edit 700 + 500 =1,200
   words per minute. Since each page is 800 words,
   that’s 1,200 words per minute ÷800 words per
   page =1.5 pages per minute. In 20 minutes, then,
   they can edit 1.5 × 20 =30 pages.


2. 20 Since the two cars are traveling in the same di-
   rection, their relative speed (that is, the speed at which
   they are moving away from each other) is
   50 − 35 =15 mph. In other words, they will be 15 miles
   farther apart each hour. Therefore, the time it takes
   them to get 5 miles apart is 5 miles ÷15 miles per hour
   =1/3 hour, which is equivalent to 20 minutes.


3. C Since there are (60)(60) =3,600 seconds in an
   hour, 45 seconds =45/3,600 hour. Speed =dis-
   tance ÷time =1/4 mile ÷45/3,600 hour =3,600/180
   =20 miles per hour.


4. C To arrive on time, the car must take t− 3
   hours for the whole trip. To travel dmiles in t− 3
   hours, the car must go d/(t−3) miles per hour.
   5. E According to the rate pyramid, time =distance
   ÷speed =(x^2 −1) miles ÷(x−1) miles per hour =

hours. Or you can pick

a simple value for x,like 2, and solve numerically.

6. D Speed =miles ÷hours. Her total time for the
   three races is x+y+zminutes, which we must
   convert to hours by multiplying by the conver-
   sion factor (1 hour/60 minutes), which gives us
   (x+y+z)/60 hours. Since her total distance is 3
   miles, her overall speed is 3 miles ÷(x+y+z)/60
   hours =180/(x+y+z) miles per hour.


7. B If the hare’s rate is amph, then he covers d
   miles in d/ahours. Similarly, the tortoise covers d
   miles in d/bhours. The difference in their finish-
   ing times, then, is d/b−d/a.


8. B Sylvia’s speed is 315 miles ÷9 hours =35 mph.
   If she were to go 10 mph faster, then her speed
   would be 45 mph, so her time would be 315 miles
   ÷45 mph =7 hours, which is 2 hours sooner.

x

x

xx

x

x

(^21)
1

11

1

1

−

−

=

( −)( +)

−

=+

speed time

distance

×

÷ ÷

speed minutes

pages

×

÷ ÷

efficiency gallons

miles

×

÷ ÷