GMAT Math : Calculating rate

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Example Questions

Example Question #231 : Problem Solving Questions

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

We need to pay close attention to some details here.

1) We are given time in minutes, but asked for an answer in hours.

2) 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.

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Example Question #233 : Word Problems

Ray travels $75 \:km$ in three hours. At this rate, how long (in hours) will it take him to travel $375 \:km$ ?

Possible Answers:

$25\:hr$

$45\:hr$

$15\:hr$

$375\:hr$

$225\:hr$

Correct answer:

$15\:hr$

Explanation:

If Ray covers $75 \:km$ in three hours, that means he covers $25 \:km$ in one hour:

$\frac{1\:hr}{3\:hr}=\frac{x\:km}{75\:km}$

$3x=1\cdot75$

$x=\frac{75}{3}=25\:km$

Perform the following calculation to find how long it takes to cover $375 \:km$ .

$\frac{375\:km}{1}*\frac{1\:hr}{25\:km}=\frac{375\:km\cdot hours}{25\:km}=15 \:hours$

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Example Question #11 : Calculating Rate

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?

Possible Answers:

400 mph

450mph

500mph

600mph

350mph

Correct answer:

400 mph

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:

3000 mi + 3000mi = 6000 total mi

To find total hours, we just have to use each leg's speed:

$\frac{1hour}{600 miles} \cdot 3000 miles = 5 hours$

$\frac{1 hour}{300 miles} \cdot 3000 miles = 10 hours$

The trip therefore took 15 total hours.

Now we simply divide the totals to find the average speed:

$\frac{6000 miles}{15 hours} = 400 miles/hr$

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Example Question #232 : Gmat Quantitative Reasoning

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?

Possible Answers:

12.5 minutes

6 minutes

25 minutes

5 minutes

8 minutes

Correct answer:

6 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.

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GMAT Math : Calculating rate

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #231 : Problem Solving Questions

Example Question #233 : Word Problems

Example Question #11 : Calculating Rate

Example Question #232 : Gmat Quantitative Reasoning

All GMAT Math Resources

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