Rates - SAT Math
Card 0 of 17
A candle burns at 2 cm per hour from an initial height of 10 cm. Write the model.
A candle burns at 2 cm per hour from an initial height of 10 cm. Write the model.
Tap to see back →
$h = 10 - 2t$.
$h = 10 - 2t$.
A car travels 180 miles in 3 hours. What is the speed?
A car travels 180 miles in 3 hours. What is the speed?
Tap to see back →
60 mph.
60 mph.
A car travels at 60 miles per hour for 3 hours, 55 miles per hour for 2 hours, and 40 miles per hour for 3 hours. What (to the closest hundreth) is its average speed over the whole course of this trip?
A car travels at 60 miles per hour for 3 hours, 55 miles per hour for 2 hours, and 40 miles per hour for 3 hours. What (to the closest hundreth) is its average speed over the whole course of this trip?
Tap to see back →
The easiest way to solve this is to find the total number of miles traveled by the car and divide that by the total time travelled.
Recall that D = rt; therefore, for each of these three periods, we can calculate the distance and sum those products:
Dtotal = 60 * 3 + 55 * 2 + 40 * 3 = 180 + 110 + 120 = 410
The total amount of time travelled is: 3 + 2 + 3 = 8
Therefore, the average rate is 410 / 8 = 51.25 miles per hour.
The easiest way to solve this is to find the total number of miles traveled by the car and divide that by the total time travelled.
Recall that D = rt; therefore, for each of these three periods, we can calculate the distance and sum those products:
Dtotal = 60 * 3 + 55 * 2 + 40 * 3 = 180 + 110 + 120 = 410
The total amount of time travelled is: 3 + 2 + 3 = 8
Therefore, the average rate is 410 / 8 = 51.25 miles per hour.
A newspaper says, 'A new medicine doubled survival rate—from 1% to 2%.' What’s misleading about that claim?
A newspaper says, 'A new medicine doubled survival rate—from 1% to 2%.' What’s misleading about that claim?
Tap to see back →
Relative increase sounds large, but absolute improvement is small.
Relative increase sounds large, but absolute improvement is small.
A person walks 6 miles in 2 hours. How long to walk 9 miles?
A person walks 6 miles in 2 hours. How long to walk 9 miles?
Tap to see back →
3 hours.
3 hours.
Definition of a rate.
Definition of a rate.
Tap to see back →
A ratio comparing two quantities with different units.
A ratio comparing two quantities with different units.
Definition of unit rate.
Definition of unit rate.
Tap to see back →
A rate with a denominator of 1.
A rate with a denominator of 1.
Formula for distance between $(x_1, y_1)$ and $(x_2, y_2)$.
Formula for distance between $(x_1, y_1)$ and $(x_2, y_2)$.
Tap to see back →
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
If 12 workers finish a job in 8 days, how many days for 6 workers (same rate)?
If 12 workers finish a job in 8 days, how many days for 6 workers (same rate)?
Tap to see back →
16 days.
16 days.
If 120 miles are driven in 3 hours, what is the unit rate?
If 120 miles are driven in 3 hours, what is the unit rate?
Tap to see back →
40 miles per hour.
40 miles per hour.
If a car travels 60 miles per hour, what is the linear model for distance $d$ in miles after $t$ hours?
If a car travels 60 miles per hour, what is the linear model for distance $d$ in miles after $t$ hours?
Tap to see back →
$d = 60t$.
$d = 60t$.
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?
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?
Tap to see back →
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
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
If a printer prints 300 pages in 10 minutes, find the rate per minute.
If a printer prints 300 pages in 10 minutes, find the rate per minute.
Tap to see back →
30 pages per minute.
30 pages per minute.
If a train travels 240 miles in 4 hours, find speed in km/h (1 mile ≈ 1.6 km).
If a train travels 240 miles in 4 hours, find speed in km/h (1 mile ≈ 1.6 km).
Tap to see back →
$240\times1.6/4=96$ km/h.
$240\times1.6/4=96$ km/h.
If a worker earns $15 per hour plus $50 bonus, write earnings model $E$ after $h$ hours.
If a worker earns $15 per hour plus $50 bonus, write earnings model $E$ after $h$ hours.
Tap to see back →
$E = 15h + 50$.
$E = 15h + 50$.
If speed = distance/time, find distance when speed = 50 mph and time = 4 hours.
If speed = distance/time, find distance when speed = 50 mph and time = 4 hours.
Tap to see back →
200 miles.
200 miles.
What is the formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?
What is the formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?
Tap to see back →
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.