PSAT Math : How to find rate
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Example Question #51 : Fractions
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
6
6.5
7
8
7.5
6.5
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
Example Question #11 : How To Find Rate
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
10
8
4
6
6
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
Example Question #31 : Fractions
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
225 miles
145 miles
1552.5 miles
120 miles
202.5 miles
225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Example Question #52 : Fractions
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
11 minutes
10 minutes
7 minutes
8 minutes
9 minutes
9 minutes
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
Example Question #32 : Fractions
If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
15 miles/hour
12 miles/hour
3 miles/hour
5 miles/hour
10 miles/ hour
12 miles/hour
The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
Example Question #61 : Fractions
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
2.7 hours
3.5 hours
2.5 hours
2.4 hours
3.2 hours
2.7 hours
Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Example Question #1401 : Sat Mathematics
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
140
170
35
210
150
140
First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
Example Question #33 : Fractions
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
Example Question #31 : Proportion / Ratio / Rate
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
36.5 min
18.5 min
25.5 min
20 min
75.5 min
25.5 min
Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
Example Question #31 : Fractions
If Kara drives a distance of m miles every h hours, how many hours will it take her to drive a distance of d miles, in terms of m, h, and d ?
m⁄hd
d⁄hm
hm⁄d
dm⁄h
dh⁄m
dh⁄m
We need to convert d miles into hours. We do so by multiplying d miles by the conversion ratio of miles to hours given in the problem, (h hours / m miles), as follows:
d miles * (h hours / m miles) = (dh )/m hours.
From this conversion of miles into hours, we see that the number of hours it takes Kara to drive a distance of d miles is (dh )/m.
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