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High School Math : How to do word problems where one quantity is unknown

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Example Question #21 : How To Do Word Problems Where One Quantity Is Unknown

Barbara lives miles from the beach, and her friend Josef lives miles from the beach. If Barbara and Joe leave their homes at the same time, and Barbara drives miles per hour, how fast will Joe need to drive to arrive at the beach at the exact same time as Barbara?

Possible Answers:

miles per hour

Correct answer:

miles per hour

Explanation:

To find the speed (or rate) that Josef will need to travel, we can use the equation $distance = rate\times time$ ( d = rt ).

This equation cannot be used for Josef yet, since only the distance traveled is known and not the time in which he will need to make the trip.

To find the time it takes Barbara to make the trip, use the same equation to solve for , where the distance is the length of Barbara's trip. Note that we express miles per hour as a fraction that represents the ratio of miles to hour.

$16 \ miles = \frac{60 \ miles}{1 \ hour} \times t \ hours$

Multiply both sides of the equation by the reciprocal of the rate. Note that the unit of "miles" cancels out, leaving only the unit "hours" (time). The result will be expressed as a fraction of a single hour.

$(16 \ miles) \times \frac{1 \ hour}{60 \ miles} = \left ( \frac{60 \ miles}{1 \ hour} \times t \ hours)\right) \times \frac{1 \ hour}{60 \ miles}$

$\rightarrow \frac{16}{60} \ hours = t\rightarrow \frac{4}{15} \ hours = t$

The amount of time it takes Barbara to get to the beach must be the same amount of time it takes Joseph to get to the beach.

Therefore, we can use this new value of and the d = rt equation to find the rate Josef will need to travel for his mile trip.

$20 \ miles = (r \ miles \ per \ hour) \times (\frac{4}{15} \ hours)$

Multiply both sides by the reciprocal of time (a fraction) to isolate the rate.

$20 \ miles \times \left ( \frac{15}{4} \ hours\right) = \left( \frac{r \ miles}{1 \ hour}\right) \times \frac{4}{15} \ hours \times \frac{15}{4} \ hours$ $\rightarrow \frac{300 \ miles}{4 \ hours} = \frac{r \ miles}{1 \ hour} \rightarrow 75 \ miles \ per \ hour = r$

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Example Question #21 : How To Do Word Problems Where One Quantity Is Unknown

What number is $30\%$ of 150 ?

Possible Answers:

Correct answer:

Explanation:

Verbal cues include "IS" means equals and "OF" means multiplication:

$n=0.30\cdot 150=45$

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High School Math : How to do word problems where one quantity is unknown

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #21 : How To Do Word Problems Where One Quantity Is Unknown

All High School Math Resources

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