GMAT Quantitative - Calculating rate

Randall traveled 75 kilometers in 600 minutes. What was Randall's per hour rate?

$7.5:\frac{km}{hr}$

$0.125:\frac{km}{hr}$

$1.25:\frac{km}{hr}$

$0.80:\frac{km}{hr}$

$8.00:\frac{km}{hr}$

Explanation

We need to pay close attention to some details here.

We are given time in minutes, but asked for an answer in hours.
A rate can be defined as distance over time.

Taking the first detail, we convert 600 minutes to 10 hours, since there are 60 minutes in one hour.

Taking the second detail, we divide 75 kilometers by 10 hours. This gives us an answer of 7.5 kilometers per hour.

A group of students are making posters to advertise for a bake sale. 12 large signs and 60 small signs are needed. It takes 10 minutes to paint a small sign and 30 minutes to paint a large sign. How many students will be needed to paint all of the signs in 2 hours or less?

Explanation

In 2 hours, 1 student can paint 4 large signs or 12 small signs. Therefore, 3 students are required to paint the large signs ( $4\times 3=12$ ) and 5 students are required to paint the small signs ( $12\times 5=60$ ). In total, 8 students are required.

Jerry took a car trip of 320 miles. The trip took a total of six hours and forty minutes; for the first four hours, his average speed was 60 miles per hour. What was his average speed for the remaining time?

$30 \textrm{ mph }$

$25 \textrm{ mph }$

$35 \textrm{ mph }$

$32 \textrm{ mph }$

$28 \textrm{ mph }$

Explanation

Jerry drove 60 miles per hour for 4 hours - that is, $60 \times 4 = 240$ miles.

He drove the remainder of the distance, or miles over a period of $6 \frac{2}{3} - 4 = 2\frac{2}{3}$ hours, so his average speed was

$80 \div 2 \frac{2}{3} = 80 \div \frac{8}{3} = 80 \times \frac{3} {8} = 30$ miles per hour.

If it takes Sally 3 hours to drive $\dpi{100} \small q$ miles, how many hours will it take her to drive $\dpi{100} \small r$ miles at the same rate?

$\dpi{100} \small \frac{3r}{q}$

$\dpi{100} \small \frac{3q}{r}$

$\dpi{100} \small \frac{r}{3q}$

$\dpi{100} \small \frac{3}{qr}$

$\dpi{100} \small \frac{qr}{3}$

Explanation

If Sally drives q miles in 3 hours, her rate is 3/q miles per hour. Plug this rate into the distance equation and solve for the time:

$\dpi{100} \small Distance = rate\times time$

$\dpi{100} \small r=\frac{q}{3}\times t$

$\dpi{100} \small t=\frac{3r}{q}$

Frank can eat a huckleberry pie in 15 minutes. His formidable sister, Francine, can eat it in 10 minutes. How long does it take them to eat a pie together?

6 minutes

25 minutes

12.5 minutes

8 minutes

5 minutes

Explanation

To solve this combined rate problem, we must use the equation: $\frac{AB}{A + B}$

Where A and B are the times it takes Frank and Francine, respectively, to eat a pie.

Therefore, it takes Frank and Francine

$\frac{10\cdot 15}{10 + 15} = \frac{150}{25} = 6 minutes$

to eat the pie.

In order to qualify for the next heat, the race-car driver needs to average 60 miles per hour for two laps of a one mile race-track. The driver only averages 40 miles per hour on the first lap. What must be the driver's average speed for the second lap in order to average 60 miles per hour for both laps?

120 miles per hour

80 miles per hour

100 miles per hour

240 miles per hour

90 miles per hour

Explanation

If the driver needs to drive two laps, each one mile long, at an average rate of 60 miles per hour. To find the average speed, we need to add the speed for each lap together then divide by the number of laps. The equation would be as follows:

$\frac{X+Y}{2}=60$

In our case we know lap one was driven at miles per hour. We substitute this value in for and solve for .

$\frac{40+Y}{2}=60$

Thus to average miles per hour for two laps with lap one being miles per hour, lap two would have to have a rate of miles per hour.

A cat runs at a rate of 12 miles per hour. How far does he run in 10 minutes?

$\dpi{100} 2\ miles$

$\dpi{100} 12\ miles$

$\dpi{100} 1\ mile$

$\dpi{100} 10\ miles$

None of the other answers are correct.

Explanation

We need to convert hours into minutes and multiply this by the 10 minute time interval:

$\small \frac{12\ miles}{1\ hour}x\frac{1\ hour}{60\ min}x\frac{10\ min}{1}=\frac{120\ miles}{60}=2\ miles$

Jason is driving across the country. For the first 3 hours, he travels 60 mph. For the next 2 hours he travels 72 mph. Assuming that he has not stopped, what is his average traveling speed in miles per hour?

$64.8\ mph$

$72\ mph$

$66.7\ mph$

$63.4\ mph$

Explanation

In the first three hours, he travels 180 miles.

$3\times60=180$

In the next two hours, he travels 144 miles.

$2\times 72=144$

for a total of 324 miles.

Divide by the total number of hours to obtain the average traveling speed.

$\frac{324}{5}=64.8\ mph$

If a plane flies the 3000 miles from San Francisco to New York at an average speed of 600 mph, and then, buffetted by a hefty headwind, makes the return trip at an average speed of 300 mph. What was its average speed over the entire round trip?

Explanation

In combined rate problems such as this, we must first find units of the desired answer: $\frac{miles}{hour}$ and then find the totals of each piece of those units. Total miles is easy as we can just add together the two legs of the trip: